UKC

Do some people not understand basic maths and how these work?

I'm currently driving daily through some road works on the motorway with a 50mph speed limit enforced by average speed cameras and there's always a few drivers that seem to fly past.

I have the cruise control set to 50mph and, yes, you gain and lose a bit against other cars, due to accuracy of speedo and tyre wear, but some drivers seem to come past at far more of a speed differential than those would account for - certainly more than the usual "10%+2" allowance the cameras would give.

Case in point being the guy that came up behind me yesterday, flashing his lights, and then undertook me, and several other cars and vanished into the distance - I assume he will be getting a note through the post next week.

On a side note, please check your brake lights - seems to be lots of cars around at the moment with at least one not working.

I guess you can go close to 60 as your average car speedo will be between 50-55 when doing only 50 plus the 10%+2 you mention.

The thing that makes me smile is when people jam their brakes on when they see the next one.... do you not understand these are average cameras?  Maybe the guy who undercut you was one of these

Cheers

Toby

Boy scout in name, boy scout by nature 😁

veering slightly, my mother in law was a group scout leader and mrs J got the last boy scout out on video (without paying much attention to the cover) when she visited us once thinking she might enjoy a movie about scouts.

Typically for your car to be doing 50 mph your speedo needs to read about 55mph. All cars are slightly different but it has been within + or - 1mph of this in every car / van / motorbike I have ever been in and compared the speedo to a GPS unit. 

Then add in human nature, we all know that if its a 50 limit the cameras won't trigger until 55 at least. 

So if your pottering along at 50 on the speedo, (45 actual ish) and other people are doing 55 actual they will be overtaking you. 

One thing I will question is how did you get undertaken? If there is enough room to be under taken you should have been in the left lane anyway. 

Based on a sample size of one, speedos are pretty accurate (+- 1 or 2 mph)  as they agree with GPS speed on my phone.

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I think the braking when they see one is often just a reflex 'oh shit, I forgot - what speed have I actually been doing?' type of reaction. I know I've done it!

Also, you should really still allow another car to pass you if you can do so safely - there are valid reasons for breaking speed limits in extreme circumstances, some of which might even allow the contesting of a fine or penalty. And even if they don't have a valid reason, it's safer not to obstruct and risk encouraging them to undertake or tailgate - you don't have to be the idiot driver to get caught up in their accident. (I appreciate this may not be easy to do if you yourself are caught in a queue in the overtaking lane.)

if the driver had awesome skills like in the movies then they only need just over a cars length gap in the inside lane to undertake dangerously.

Of equal irritation I find are the people who sit in lane 3 with no slower traffic to their left, driving along at 45mph completely in their own world.

Those who brake for each and every average speed camera before zooming off do make me chuckle though. I've always wondered how many go on to discover the meaning of 'average' by way of FPN in the post. The thought is almost as satisfying as the one time someone joined the M1 about 6" from my rear bumper, quickly took up permanent position in lane 2 and zoomed off at about 90mph...to be immediately flashed by a speed camera.

I spent the last 2 years driving up and down the m6 several times a week, I used to match the speed of the lorries, some sections I would drive at 50 -55, other sections just drove at normal speed. Never got any speeding tickets. 

A friend in the know reckons that the software used in average speed camera systems can't place a car's position with a great deal of accuracy. Therefore since it can't be sure exactly where you were when your speed was read, it can't be that accurate about your average speed. He reckoned that to err on the side of caution, you wouldn't get done in a 50 avg speed zone unless you were doing around 65.

Disclaimer. I haven't tested this theory, and I don't know what software advancements have been made in the several years since.

I'm never really sure what to do when I've been driving at the speed limit in the fast line and a "congestion stay in lane" followed by speed restrictions section starts. Because a lot of other people ignore the speed restrictions I'm obviously going slower than people to the left of me. But the gantry signs keep showing "stay in lane"...

Yes, you are right, mechanical speedos always had the over reporting issue built in to ensure they never under read, however more modern cars tend to use GPS devices etc and therefore have a much smaller margin of error.

Yes. Having checked my own car's speedo against 2 diff GPS devices it's only 2mph over at 60mph.

Almost certainly. I bet a good quarter of the population couldn't give a reasonable hand-wavy definition of 'average'. By contrast there can be barely a driver on the road doesn't know what a speed camera does.

Or it's not his car/plates.

jk

Given that average speed is calculated by dividing the fixed distance between two adjacent cameras by the time between passing those cameras which are generally a couple of miles apart, I don't see how an error of a few meters can make a significant difference to the calculated average speed.

Does anyone else find themselves avoiding roads with these things installed on them?

I checked mine against the GPS - also found my speedo was stating 2mph above GPS. So in average speed areas I set to 3 or 4 mph above the speed in question. helps that my cruise control is "adaptive".

No, they're brilliant. If the speeding pillock has any idea of the meaning of average then they will drive at a reasonable speed, and it makes life more pleasant for everyone on the road. I firmly believe they should have been installed where speed cameras have been permanently installed on the motorways, in place of the normal type that they installed. They're a menace - they encourage people to slam on the brakes at every overhead gantry before continuing at their previous speed.

There should be no +/-, only +.  It's a legal requirement* that your speedo should never indicate a speed slower than your actual speed.  It's allowed to indicate a faster speed though, for any true speed between 40-70mph up to an upper limit of the true speed + 10% + 6.25mph.

So in practice, all car speedos indicate a slightly higher speed than you're actually travelling because that's allowed and it's the only way to be sure they'll never indicate a lower speed (which isn't allowed) on account of tyre sizes, wear & tear, inaccuracies in calibration etc.  Maybe the GPS speed on your phone is over-reading as well. 

At a true speed of 50mph, your speedo could legally read 50 - 61.25mph.  If the speedo reads 50mph you could actually be travelling between 39.8 - 50mph.  Reading 50mph when you're actually doing 45mph would put your speedo just about smack in the middle the legal range.

*Link for the above if you don't want to take my word for it.
http://www.legislation.gov.uk/uksi/2001/25/schedule/3/made
(Scroll down to section 19: "speedometers")

There used to be an idea that th cameras covering each of the lanes didn't talk to each other so that if you entered the controlled area in lane 1 then left in lane 2 you'd be OK but I bet that's not the case any more.

I'd be more inclined to think that the drivers who pass you at ridiculous speeds are the ones who aren't taxed, licenced or insured (10% of drivers, we are told) so they don't care a toss anyway.

It’s alright, you can drive as fast as you want so long as you do sudden panic breaking every time you see an overhead camera...

I don't see why not.  There are millions who don't know what their indicators or for, or how traffic lights work, which lane is which, etc..

One day, I gave up trying to go faster, sat four seconds behind a lorry and set my cruise control to match.  Nobody got into the space in front of me, nobody tailgated me for more than a second or two before pulling out. If I can’t drive at 2 am, I now sit with the lorries and enjoy stress-free motoring on the motorways that is as safe as it can be for the conditions.

Each to their own but I get bored and my attention wanders.

I think that on the horribly congested roads South of Manchester there is an argument for ensuring everyone drives at a similar speed.

On uncongested roads I find that vehicles travelling at differing speeds don't interfere with one another very much.

I look forward to the dawn of the autonomous vehicle. What better way to get to Glencoe than to chuck your rucsack in the boot, put on decent album, crack open a can of Stella, spark up a joint and set the controls for the heart of the sun (or probably the Kingshouse)..

I don't have a problem with, errr, 'responsible speeding' on motorways - but some of the behaviour you see on the M1 and M25 defies belief. Cars regularly going past at what I estimate is upwards of 100mph, weaving in and out of traffic in all lanes to make progress, sitting 6" from someone's bumper at speed because they have the temerity to use lane 3 to overtake slower traffic and aren't going 90+mph. I'm all for any measure to curb their behaviour because I refuse to accept that the most dangerous part of any climbing trip I make is getting to the crag.

During my one experiment using the Waze app on my phone for navigation instead of Google, I noticed that the Doris would "warn" me about a speed camera at pretty much every camera within an average speed camera zone.  Waze uses crowd sourced data so these warnings will have been based on input from users who obviously do not grasp the concept of "average speed".  (They were quite probably also using their phone illegally when they logged each camera on the app.  My phone was sat in the cubby netween the two front seats, with the Doris talking to me via Android Auto.  No input from me once I'd set up the destination and told it to start navigating.)

I also noticed that many of the traffic volume monitoring cameras would trigger a speed camera warning from Waze.

I gave up using Waze after that journey.

Speedo checked against 2 GPS devices - phone app and Garmin - and it's only about 2mph over real speed, in accordance with what DeepSoup said. And that's with pretty worn tyres that are due to be replaced. Car has built-in GPS, not sure if the display is taking a feed from that or mechanically from the engine.

But I'm "pottering" along at 50 actual, not 50 on the speedo, and they still seem to be going a good lick more than 5mph faster.

Ended up in outside lane due to passing a lorry and stayed there, as I could see another lorry slightly further up in the same lane. In any case, the guidelines state you should minimise changing lanes in road works - shouldn't be a problem with everyone doing the same speed, anyway. He nipped up the inside and got lucky as that lorry moved back left.

I say +- 1 or 2 mph because I find driving distracts my concentration from Facebook let alone comparing GPS speed & speedo (joke).

The +- reflects my estimate of the discrepancy between transient GPS digits and a quick glance at speedo needle from the passenger seat. It doesn't represent the law.

I don't remember ever seeing anything more than 1 or 2 mph difference between speedo needle and radar speed signs either so  I reckon the speedos are much better than the legal requirement of V/10 + 6.25 mph.

I'd need to look again to determine if the speedo is legally overestimating or illegally underestimating the speed.

"At a true speed of 50mph, your speedo could legally read 50 - 61.25mph" - my suspicion is that this law reflects what was an achievable standard long ago and that current speedos will show 50-52mph.

My Chiropactor (whom you would have thought would have a reasonable level of intellect) could not grasp how he got a FPN through 50mph roadworks.

The first 2 or 3 he was travelling at ~20mph due to congestion, when this cleared he sped up to >60mph for the remainder figuring it would all average out over the entire control zone, completely missing the point of why they are there in the first place.

Out of interests what car do you have.  I've got a vw van and golf and both read over compared to a gps, the thing I find interesting is the error seems to increase with speed so a low speeds the error is only 1-2 mph but up to 5mph at motorway speeds.  Could this be lag in the gps I wonder or deliberate in the car speedo?

Cheers

Toby

Why would you think that? If they believe in Chiropractic, they could believe in anything.

While I remember, this seems relevant:

https://b3ta.com/board/8500619

I imagine that the error is a percentage of your speed, rather than a fixed offset.

2005 Astra. I've not checked at motorway speeds. 

At a steady speed any lag between GPS & speedo shouldn't matter. If the legal standard is V/10+6.125 they will manufacture to a tighter specification (eg V/20+1). Hence a speedo that deviates a bit from the tighter spec is still well within the legal spec. 

In my car, if the speedo is showing 80mph then I'll be doing 70mph (as confirmed on a regular basis by GPS over a decent stretch of flat, straight road).  Then again, I run smaller than OEM wheels and tyres although, importantly, they are still one of the type-approved sizes for the car.  This is something else that manufacturers need to take in to account when calibrating the 'error' in the dash speedo. (It also messes up the MPG calculations in the trip computer, though those are never very accurate anyway.)

My experience of 50mpg average speed zones is that with the cruise control set to 50mpg according to the GPS I go slightly faster than some other drivers - in which case usually I nudge my CC down a notch rather than bother trying to overtake, although there are occasional nervous nellies doing 40mph who are better left behind when it's safe to pass.  I can't actually remember ever being passed by someone going significantly (e.g. 10mph) faster than 50mph.

What I find intriguing is the average speed cameras on the A9, which cover both single and dual carriageway stretches.  As far as I can see they don't have a camera at each change, which implies that someone has sat down and done the sums to work out the fastest legal transit times for each segment, including making some sensible allowances for accelerating and slowing down at each transition.

Based on a sample size of 13 different make and model vans, the wife's car, my mums car, 6 different make and model motorcycles and 3 trucks with a tachometer across 3 different sat navsI found the following.

All the cars and vans were between 7 and 9% over read including the 19 plate vans I just bought. The motorcycles were closer to the 7% over except 2 different BMW bikes I have owned, both were within 2% at 70 mph. The trucks with tachographs were that close to the GPS that I couldn't detect a difference. 

I don't know - you'd have to assume that if he had a reasonable level of intellect then he might have managed to qualify medically...

I don't know but I would guess it's more likely they'll just be set to catch anyone exceeding the higher limit across the entire stretch.

I know and it really bugs me. One day one of those idiots is going to smash into me

In my youth I was seriously injured in a car smash as a passenger by the driver, my "mate" [not], driving like an idiot and writing the car off, losing control. It turned out he was uninsured (I didn't know that). The crash has negatively affected my life

Doing the maths on this one if camera 1 reads your plate 5m late and camera 2 reads 5m early with a distance between the two cameras of 1000m would give an impression at 50mph that the vehicle was travelling at 50.5mph based on it taking 44.7205 seconds to travel 1000m at 50 mph.

If you increase the distance between cameras the error decreases, say a section with only two cameras at 4000m would give an error of 0.125mph using the same early/late reading.

Google uses the same data as Waze for speed cameras and gives you the same warnings (unless you have them turned off).

If you are a passenger, you can click on the cameras, roadworks, congestion etc and it will tell you that it was reported via the Waze app and when.

The bizarre thing is that they have not yet merged the directions and live traffic conditions. Have them both running at once and they will disagree on the best route and current traffic conditions.

Or they don't actually do anything, they could just be there as a deterrent? 

That, surely, is about 20 minutes work with a calculator...

No, the A9 system between Inverness-Perth is only on the single carriageway stretches. This was clearly announced when the system was installed, and I have extensive empirical evidence that they don’t cover the dual-carriageway stretches. Whether there may be a camera van on those is another matter....

Er...

Last time I went that way, I spotted an unmarked Volvo.  Who expects that?  Round my way it’s all black BMWs of a specific model and 1-2 years old which is at least predictable.  But a Volvo?!

Here's a good question to test real understanding of "average speed":

The speed limit is 30mph. Half way between two cameras, you realise you have been doing a steady 40mph. At what steady speed do you need to drive the second half in order to get your average speed recorded down to 30mph?

 I suspect that it would show that about 95% of the population don't really understand it!

Mostly up here they seem to use BMWs and Audi’s for unmarked work these days but I can definitely remember they used to have some Volvo T5 estates. Worth keeping an eye open for, thanks.

On our old 2005 X Trail the speedo reads 50 and actual (GPS) speed is about 45. On our newer (2011) Volvo the speedo reads 50 and we are doing 49 and the difference does not increase even up to 70, so I'd agree that they seem to be more accurate now.

Aww gosh.  I parted with my 2005 X-Trail last year as it got to peak rust. I miss the engine rattle...  

Go on. I'll fall for it. I suppose 20mph is wrong...

My understanding is that those drivers going well over the average speed limit are just planning on turning off the road before the next camera.

Good question!

Obviously the answer is 25mph!

Just off the top of my head, no pen and paper, calculator and whittling it down by trial error at all, no sir, not me! 

24mph?

I normally like average speed camera zones. So long as they’re very occasional. It’s a chance to catch up on Facebook and texts etc. Normally when you average 90 you can only do phone calls.

I've nudged the speedo to 60 in average speed cameras and no letters yet.

I don't think you were undertaken though; I think you'd become a queue and their lane just happened to be moving quicker...

North of Perth the average speed cameras cover only the single carriageway. The dual carriageways are covered by normal speed cameras or camera vans. South of Perth the dual carriageway has average speed cameras, so the A9 system is inconsistent.

Is that the little hamlet next to Castleton? Lovely place - but how did you get home?

You were right to be suspicious:  youtube.com/watch?v=ZIO-ExZVkdw&

I had to look it up as I also immediately thought "20mph obvs!", then thought he wouldn't be asking if it was that easy

Nice - I've not seen that problem before. Made me think, once I realised the answer isn't the obvious one!

A variant (not for you as you'll know already):

If, while driving along a road with a 30mph limit between camera A and camera B, I spend half my time driving at 40mph and the other half driving at 20mph, what is my average speed between A and B?

Like ball bearings in a bean can! Proper old school diesel. 

I got done doing 57 in a 50 in Wales 

Here’s a bit of a head scratcher....

on a two mile journey, you do the first mile at 30 mph. What speed should you do on the second mile to average 60 mph for the journey?

Surely it's not possible? 60mph for a 2 mile journey (not a standing start I've assumed) will take 2 mins (1 mile per minute), at 30mph the first mile will have taken you 2 mins, so you can't catchup, (within the bounds of physics).

Sadly there aren't great alternatives to the A9. I do find that having to watch my speedo closely does distract from other driving though. Fine if you have modern functions like cruise control, or an old enough vehicle where the rattles change with speed! Current van isn't rattley enough yet but not of cruise control generation!

This is me. In my younger days I was in the fast lane sat up someone's arse swearing at them to get out of the way but for the last 20 years I have been steady away. 

60 to 65 on the motorways. It makes bugger all difference to the journey time but rather than being wound up all the time I'm chilled out. My new van has a driver setable speed limiter. I set it to 75 mph which equates to 69 ish on my GPS and its very rare I feel it kick in. 

Added bonus is at that speed I get 34mpg out of my large 3.5 ton van that is loaded to 3 ton all the time. 

I’m waiting for the day when adaptive cruise control starts to appear on white vans. Nothing else could so easily improve road manners and stress-related safety. Except full autonomy, but that’s a way off. 

Depends what you mean by half way. The 30mph relates to both distance and time.

So do you mean half way in distance or time?

As it's a mathematical exercise, infinitely fast would be correct?

Yes, this is the usual, easier version! I usually use the example of a plane flying from A to B against the wind, and then back with the wind behind it.

I meant half way in distance.

But it is a very good point. I deliberately didn't specify whether I meant a time-average (presumably assumed), for which the answer is 24mph (less than 30mph because more time is spent at the lower speed) or a distance-average, for which the answer is 30mph (because equal distances travelled at each speed).

So, the correct response to the question from someone who REALLY understands averages is to ask whether I mean a time or distance average.

I think white van man gets a bad rep these days to be honest. Certainly on the motorways even though I'm doing 65 it's not often I'm overtaken by a van. The worse culprits who pass me that fast it seems like I'm standing still is the mid to high range rep mobiles, over sized saloon cars. 

"I meant half way in distance.

But it is a very good point. I deliberately didn't specify whether I meant a time-average (presumably assumed), for which the answer is 24mph (less than 30mph because more time is spent at the lower speed) or a distance-average, for which the answer is 30mph (because equal distances travelled at each speed).

So, the correct response to the question from someone who REALLY understands averages is to ask whether I mean a time or distance average."

Makes it sound like you are in the 95% (when you are probably not). When in a hole it's best to stop digging

Why on earth do you say that? My question had two points. Firstly to see if people understood that an average could be over time or distsnce. Secondly to see if, having assumed we are averaging over time (which is what speed cameras do), people got the correct answer of 24mph.

Extension exercise for the mathematically inclined:

Prove that, for any journey, with speed varying in any way, distance average of speed is equal to time average of squared speed divided by time average of speed.

Thats for people who really understand translating words to maths.  For people who understand averages it’s “which average” - eg geometric mean or arithmetic mean? The concept of “average” is very underspecified.

If you could immediately change speed - 20mph.

However as you would need to slow down (or brake harshly !), more like 17 or 18.

Do average speed limit cameras actually do anything? They are very effective in slowing people down, but I have never met anyone who has been caught by an average speed limit camera, so I have wondered whether they are just a deterrent rather than something that actually clocks speeding motorists.

Have anyone on here been caught by one?

"Half way between two cameras, you realise you have been doing a steady 40mph."

The question only makes sense if you're talking about half way in distance terms.  Half way in distance between the two cameras is a point in space and as such it's possible to know you have arrived there when you arrive.

You can't suddenly realise you are halfway through your journey in time, because there is no way to know you are there while you are actually there - you only know where the halfway point was retrospectively after you have completed the entire journey.

E2A: Have you heard the old joke about an economist, a physicist and a mathematician on a train to Scotland?

Shortly after crossing the border they look out of the window and see a black sheep in a field. 
The economist says "Oh look, the sheep in Scotland are black." 
The physicist says "You can't assume that, we only know that some of the sheep in Scotland are black."
The mathematician sighs, rolls his eyes and says "There is at least one sheep in Scotland, at least half of which is black."

The A9 cameras north of Perth are certainly active and working. At least around Bankfoot, I know a rising number of people fined and awarded points by post. 

That said the cameras in that section they had before the current dualling roadworks didn't differentiate between cars and vans so everyone could do 60 on the single carriageway.  I've also heard from a few people that many of the fixed average speed cameras are turned off due to not enough processing power... But as a driver there's no way to tell.

It's possible... you know from experience of the road its a 5 mile stretch with cameras and you know the time you started (from say the start of a distracting news on the radio) and then you realise from the current time you must have been doing 40 for five minutes.

Here's one for you:

I arrive on the M40 20 minutes before work, which is 5 minutes beyond my exit (so 15 mins on the M40). My exit is 17.5 miles away, so I need to average 70 mph. I am confident the road will be reasonably clear.

How long should I spend behind a lorry to minimise total fuel consumption?

That isn't knowing, it's a prediction that may or may not turn out later to have been correct.  Some predictions are better than others but in the real world you cannot know with absolute certainty from experience what will happen in the future.

Also it is circular - if everything does go to plan and your journey goes exactly as you have experienced it in the past, you still did not arrive at the halfway point in time.  You arrived at some arbitrary point and by choosing to adjust your speed accordingly retrospectively made it the halfway point at the completion of the journey.

Although the question goes on to say that you are going to average the speed limit over the whole stretch, so you can calculate in advance how long the stretch will take. you are half way in time when half this time has passed.

Bonus question:

When you realise you've been speeding for half of the projected time and then instantly brake to precisely half of your former speed to compensate in the one-third remaining distance, how many of the cars around you will also brake hard, assuming you must have spotted an unmarked plod?

It does, but I refer you to the circularity I mention above - you don't have a sudden realisation that you've arrived at the halfway point, you arrive at an arbitrary point and by the decision you make there choose to make it so.  We're not really discussing maths here, we're discussing grammar (or perhaps semantics).  As you phrased it, your question was not really ambiguous between the halfway point in time or space; it clearly means space.

To make it truly ambiguous, I think you would need to phrase the question so that it was not necessary to know where the halfway point was before the journey is complete.  Eg:  "You drive between two speed cameras at an average speed of 30mph.  Having driven at 40mph for the first half of your journey, what was your speed for the second half?"

I was once tailgated beyond belief by a van man on the M1 because I dared to use lane 3 to overtake slower traffic. Flashing lights, so close I could barely even see his headlights.

Top tip: if you're going to do that sort of shit, don't put your mobile number on the back of your van. The subsequent (hands-free) phone call was most satisfying.

Good luck with that.

If the cameras face in the direction of travel, how hard do you have to brake for the car behind to be so far up your arse that the camera can not see your number plate?

The time to drive a fixed known distance at the 30mph speed limit is known. You can know you have used half that time driving from the start point at 40mph. It's not a prediction or circular.

59 in a 50 and 33 in a 30 in east Anglia for me, both 'normal' cameras. The days of 10mph+10% are over where cameras are concerned.

The question was phrased thus: “Half way between two cameras, you realise you have been doing a steady 40mph.”  

This strongly implies the driver had until that very moment been unaware of their speed during the first half of the journey.  Unless they are highly serendipitous it seems very unlikely they could have been half way in time, and unless they were also a good mental calculator it seems very unlikely they would know they were half way in time.

A poorly worded attempt at a trick question is my view. (Edit: sorry, Robert!)

Yes. I think that is the point I made (less clearly) in my last post.

There's a motoring lawyer specialist on Pistonheads (driving forum) that has, for years, offered to represent free of charge anyone caught below those guidelines. So far nobody has EVER taken him up on it or been able to produce a NIP for 33 in a 30.

I'm not saying I don't believe you but yours could be a first!

Of course it's a prediction.  You can't know when you have used half the time until you know how long the entire time was.  If you've done the journey a hundred times before you might have a very reliable prediction of how long it is going to take, but today there's a tractor turning into the field entrance that you never took much notice of before and it turns out what you thought you knew five minutes ago was wrong.

Even so they didn't know they were half way in time, they did their mental calculation, came up with a plan and put the plan into effect to make it the half way point in time.

Agreed.  

There is one interpretation where this isn’t the case, which is where the driver picked a fixed length of time for travelling between the two cameras and had a stopwatch on the dashboard to inform them of the half-way point.  The old 3 litre Ford Granada had a stopwatch mode on the clock by the rear view mirror, but insurers took an increasingly dim view of such fixtures and they’re out of fashion these days...

Yes, I find myself travelling up the A9 less frequently than I used to, preferring to head up the West now.

Before their introduction I travelled up and down the A9 pretty much once a fortnight for quite s few years. I reckoned that the average speed then was 75 mph. If you drove at less than that speed a queue formed behind you. Except for 4 or 5 black spots, mainly badly designed junctions, travelling at that speed was perfectly fine. I'd far rather that speed restrictions at the black spots were enforced, possibly taking the limit down to 50 mph to force drivers to take heed than enforcing 69 mph for over 100 miles. There's nothing more tedious than sitting at 60 mph on a November evening on a straight road with nothing else within a mile of your vehicle.

OK, I must have missed that.  From my (not 100% rigorous I'll admit) observations last month, it's not as if there's an average speed camera at the end of each dual carriageway section, which is what I'd have expected if they were being deployed that way.

However, information duly noted for next time...

In reply to girlymonkey:

They certainly seem to work for that purpose.  The incidence of idiotic driving seems to be much lower these days, even on the dual carriageway sections which, as noted above, aren't covered by the average speed cameras anyway.  (Though you still get some folks who do 80mph+ right up to, and beyond, the point where the two lanes merge, MGIFing their way ahead of as many people as possible in order to...join the 50mph queue behind an HGV on the single-carriageway section.)

In reply to Eric9Points:

Depends where you're heading to, obviously, but isn't it significantly slower heading up the west side?  I have in the past done Edinburgh to Fort William via the A9/A889/A86 route because it's quicker - or, if nothing else, you're less likely to get held up by a dawdler on a stretch where passing really isn't a sensible option - than on the M9/A84/A85/A82 route.

Isn't part of the problem with the A9 the fact that there aren't many truly straight sections?  The flawed rationale behind turning it in to a series of long curves back in the ?1960s? was to allow people to drive faster by taking out the tight bends, but they ended up managing to put the limit of clear visibility of the road ahead pretty much exactly at the "point of indecision" where it's difficult to see whether or not you do have time to overtake safely, just in case someone does appear from around the bend doing 60mph+ in the opposite direction.  Hence people end(ed) up frustrated and eventually decided to "go for it" anyway, which has a high probability of things not turning out well.

I wasn't aware of that.  Looks like the function only become available this year.  Knowing this now, I am still unable to find out how to activate the function (or the speedometer and current speed limit functions, which are also supposed to be available now) in Google Maps, never mind turn it off!  It's certainly not giving me warnings, I'd have noticed if it was.  All I get is the voice directions.  I'm running the latest version of Maps from the Play Store.  Odd.

(I also missed the fact that Google actually acquired Waze back in 2013.  Not being a Waze user it obviously passed me by.)

But the same goes for distance!

Are you aware of this..?

https://www.transport.gov.scot/news/a82a85-average-speed-cameras-to-be-intr...

Plans have been announced to install a £250,000 average speed camera system on a 15.9 mile stretch of the A82 and A85 roads between Tyndrum and Lix Toll.

https://a82-a85road.info/

One thing that I would like to know is how do they work when you go through a number of them on a long stretch. Do they calculate your average over each section or just the first & last?

Over each section

What's the point? You never get past 40 with all the camper vans etc! I hate those roads. And then you get the crazy overtakers who are intent on killing themselves and others(which average cameras won't stop as they will still want to go faster than the camper vans). I'm glad I don't need to use it as often as I used to.

I often use that section to overtake the campervans I've been stuck behind heading up Glen Ogle or down from Bridge of Orchy. So I'm probably part of the problem they're trying to solve...

I'm tempted to think that it'll mean more careless overtaking on the five stretches of main road approaching this (Glen Ogle, the A827 from Killin, Glen Falloch, Glen Lochy and coming over the pass from Bridge of Orchy), but I suppose we'll see.

If it were just the first and last then installing and maintaining the central ones wouldn't be great value for money!

But it won't solve it as people will still overtake the campers there as the discrepancy in speed between cars and campers still makes it worthwhile. You wont be above the speed limit for long enough to affect the average for the cameras

Yes.  But in distance any decision you make about how fast you are going to travel from that point onwards does not alter the position of the half way point retrospectively.

I could put up a marker post on the route equidistant from A and B, you could see it as you drive by and suddenly realise you are halfway (in space) - nothing you subsequently do to moderate your speed will change it's position.

In time you would have to suddenly realise that you are at a point where, having done a steady 40mph thus far you have the opportunity to moderate your speed to a different steady value and complete the journey in the same time again that you've travelled so far whilst simultaneously doing an average of 30mph over the entire journey.

In both cases there are assumptions, but the latter requires more assumptions than the former - that the calculation is done correctly, that the calculation is done instantaneously, that the car decelerates to its new steady speed instantaneously.  (Both cases require the journey to be completed, of course, and for A and B to stay in the same place relative to each other in the meantime.)

In putting your maths problem into words, you also deal with the English language.  The way you phrased the question was not ambiguous between space and time, whether you intended it to or not it clearly implied the mid-point in space.  I gave an example further up of how it might have been phrased differently so that it would have been ambiguous.

I found Robert's and then, later, John's expression of a different version of the problem completely unambiguous. Robert's was easier to solve but in neither case did I have to recourse to nuanced layers of mathematical learning to get (what I very much suspect are) the intended answers. Language rules.

Yes but I was thinking of long stretches with intermediate junctions. The M6 is like this where they are doing the Smart motorway upgrade.

No I wasn't.

How depressing to think that the drive hone on a Sunday night will get longer and more unpleasant. Stuck behind a convoy of camper vans for miles.

Weird.

I found all the new features were activated automatically when they were introduced so I'm guessing your version doesn't have them. Old version of Android maybe?

Over each section. But not all cameras are functioning all of the time so some sections will be longer than 2 cameras.

Not that that would change the way you drive, unless you love gambling.

Here's my tuppence worth on average speed camera strategy as regularly used on the A9 Narcoleptic Zone. 

If the road is pretty empty or light car traffic then probably I have cruise engaged at 60-ish. Do I push it to 10%+2? I have no comment at this time; but read on.

I have the computer displaying average speed. At every average speed camera, I reset the trip for the average speed computer. Well, it's something to do to relieve the mind numbing boredom apart from anything else. Thus I have a constant display of my average in this section. 

If I have been behind a truck at 56mph (they are all 56 flat out against the calibrated limiter since 50+10%+2=57) for 5 miles then there is probably enough slack in the system to minimise TED (Time Exposed to Danger) when overtaking it and then complete the section like a normal human being instead of a mindless zombie.

If I have been behind an Italian motorhome convoy at 35mph for half of the section then there is enough slack in the system to use all available resources (min TED!) when overtaking them and still coast to end of the section inside of 60mph average. 

I have all the camera positions mapped out but so far I haven't put the time in to work out how they are paired up. Some sections are now compromised by new dual carriageway construction, but unless the pairings and setup are know, road users would be foolish to assume there is no enforcement. 

You are correct. When I was working with a consulting office that also did some highway stuff back in the 90s, they had a copy of a Scottish Office report that discussed that point in some detail. Several years later, when A9 deaths were a hot topic, I visited them to borrow it but they no longer had that copy. I approached the Scottish Government without any useful result. I then approached the late John Farquhar Munro MSP (vested interest: Allt a'Chruinn to Holyrood every week!) who had no more luck than I had. All mention of the A9 being built to an already discredited design philosophy had mysteriously vaporised. Probably coincidence. 

This is a real problem. The DfT numbers in the annual reports (RRCGB) clearly show that not paying attention is killing about 10 time more people than breaking the speed limit. The rate of road death is now a quarter of what it was when I was growing up, in spite of the higher traffic densities, but for many years now the numbers have stalled at around 1700 per annum. 

These numbers are stalling after we have just spent 20 years obsessing about speed limits and doing very little about the most dangerous driver behaviours. 

We now have electronic systems that will easily catch you out if you don't have cruise control or limiters and just drive to the conditions. If, on the other hand, you do have cruise control, how engaged are you with your driving? I get concerned about this regularly. If it's an issue in a car, try driving a truck for 4h30min. Limiter, cruise control, collision detector, anti-roll, AEB, and so on: not only enough automation to save you if you fall asleep but it sends you to sleep.

Link please?

You have my sympathy.  When I was a toddler my dad was seriously injured in a car crash not his fault (bus failed to give way at a junction).  He suffered head injuries that affected the rest of his life.  In addition, it practically ruined my mother's life as she stayed married to a man who ended up a stranger, and not always a nice one.  It also has had significant (detrimental) lasting effects on myself and my older brother. 

Sadly, idiots who drive recklessly either seem not understand or not to care about the havoc they potentially reek on the lives of others.

Thank you for reminding me. The 2018 number were due a few weeks ago. Last year they were 3 months late and the current state is that some documents were put up on GOV.UK a few days ago but I cannot see the full report.

https://www.gov.uk/government/statistics/reported-road-casualties-great-bri...

"1,782 reported road deaths, similar to the level seen since 2012" 

What was evident in last years report was the flat-lining of the total fatalities number, and the same pattern of "contributory factors" as the previous couple of decades. That pattern is that two groupings of factors, not paying attention and making a poor judgement above others course or speed accounted, accounted for the majority of the fatalities. 

Last year there was blatant manipulation of the top ten list. Previously, 'exceeding the speed limit' had NEVER made it into the top ten. Last year, a factor that had been at the steady 7% for years or decades, 'following too close', seemed to completely disappear from the British drivers' list of dangerous habits! It's a miracle, surely! Equally miraculously, it was replaced in the top ten by 'exceeding the speed limit' (still at its all-time high of 5%, when once it was 3.5%).

What could this mean? It could mean that the numbers are corruptly manipulated. Alternatively, it could mean that all of the speeding enforcement of the last twenty years has had no effect whatsoever (maybe it's even making things worse). 

The things that are really leaving about 1000 people dead each year who could still be alive today, not paying attention and making a poor judgement above others course or speed, are exactly the subjects that Road Policing officers are world-class expert in. Instead of using their expertise to assist the driving public to improve their driving and potentially save hundreds of lives, these guys are stuck in a layby with a laser gun, bored out of their minds. 

Yet there has been a very significant decrease in fatalities on the A9 since the installation of speed cameras. You do seem to be in denial about this.

The A9 has been a much pleasanter road to drive since the speed cameras were introduced. You can make perfectly good progress and there is far less of the crazy dangerous overtaking (there being no point).

My original problem was not meant to be ambiguous as to whether "half way" meant half way in distance or in time (I doubt anyone would have taken it to mean time). The point was that the common incorrect answer of 20mph is wrong, but would in fact be right if "half way" was in time rather than in distance (assuming that we are talking about a time average as is in fact being measured by cameras rather than a distance average - in the case of a distance average, the correct answer would be 20mph for half way being in distance).

Unfortunately, cause and effect cannot be reliably established. This was always going to be true. It would have been wise for Government to get a grip on that from the start.

Four significant things have happened. 
- average speed cameras were introduced (with the assumption that this will reduce speeds)
- the truck speed limit for over 7.5 tonne is increased from 40 to 50 (de facto 56!!!)
- new lengths of dual carriageway have opened
- major lengths of road works have been established with additional traffic controls

Two of those have reduced speed.

Two of those have increased speed. 

It's nothing to do with the time you might take overall. You took 5 minutes @ roughly 40mph in my scenario and so need to slow to 20mph for the next 5 minutes to make an overall average @ 30mph. Sure you can't guarentee the future but you know that is the requirement given the situation at halfway. You can't guarentee the future in the half distance scenario either ! It is simply no more a prediction or a circular agument than the other case . Maybe Robert was more prescient than I expected, despite his slightly unclear explanation.

I could argue that, for those with good mental arithmetic, knowing half time is easier than knowing you are halfway in distance but then again knowing exact speed isn't so easy, even if some people do seem remarkably constant from their throttle positions (and sound input from the engine revs).

The model of phone dates from 2015 (though I'm not sure how old this particular one is).  It's running Android 7.1.1 Nougat which according to Wiki is still "supported" (whatever that actually means).  Given that the warnings in Waze work on this phone, there would seem to be no technical reason why they shouldn't in Maps.  Odd.

I've just checked again and Maps does have the speedometer setting, which AIUI was introduced at the same time as the speed camera warnings.  Can't recall ever seeing the speed indication on the screen though.  Maybe it only displays on the phone screen not the ICE head unit via Android Auto, which is how I usually use it.  I'll make sure to check this weekend when I'm heading up north again.

TBH I'm not that worried about not having the speed camera warnings.  My one experiment with Waze suggested that it gave an annoyingly high number of false positives, especially since I am consciously more diligent about staying within the limit anyway these days.  (Perhaps it's useful to have something like that to keep me occupied and alert when the road and the car are conspiring to send me to sleep.  Apparently.)

You mean a bit like smoking and lung cancer? Carbon emissions and climate change?

You are definitely in denial.

Of course speed in itself is never the direct cause of an accident - if all vehicles could travel a constant safe distance apart at a steady 100mph there would be no accidents. The point is that the speed cameras have changed driver behaviour in ways to reduce other causes of accidents (such as reckless overtaking) and, of course, when unexpected shit does happen, accidents at lower speed will be less severe.

They obviously do. Have you not driven up the A9 since the cameras were introduced? Traffic, in the main now moves at a steady 60-65mph.

The idea is that this tends to equalise speed between cars and trucks, thus reducing the tendency to overtake, especially when frustrated.

There have almost always been roadworks at some point on the A9 pre or post cameras.

I have to admit (much as I don't want to!) that it does seem clear that the average speed cameras have both improved safety on the A9 and made traffic flow steadier and more reliable. It may even be the steadier flow that's mostly responsible for the reduction in accidents, rather than the reduced speeds. I don't like them, but that's probably just irrational and selfish, as the evidence in favour of them is quite striking.

The point Jim made there about the 7.5t lorries is a fair one, though - it's quite possible that allowing them to go faster has made the road significantly safer, reducing the amount of risky overtaking. And as this has happened at the same time as the average speed enforcement, it may not be possible to tell how much of the improvement comes from which change.

Yes, that is exactly the point I made. The capping of speeds has encouraged steady flow without crazy overtaking.

And that is precisely the other point I made - the combination of cars going slower and lorries faster has steadied the flow. But Jim seems to be perversely determined to twist this point into an argument against the speed cameras.

Given that the cameras have certainly made the A9 significantly safer, I think it would undeniably be selfish to argue against them. In moderate to heavy traffic, it is now a much less stressful and only slightly slower journey. I do, however, agree that it can be a bit frustrating when the road is empty at night!

There’s still confusion in some minds to the speed limit on a dual carriageway. 

I was behind a driver doing 60mph in the outside lane last night with a muppet tailgating me. Inside lane had just emptied at the off slip. After a couple of minutes I flashed the guy and he moved over, at the same point the guy behind me decided to undertake us, finding himself now stuck behind the first car which had moved into the inside lane. 30 seconds later he’s back out behind me tailgating me and before I had a chance to be a safe distance past and pull in, he aggressively and dangerously undertook me. 3 mins up the road I caught up with him stuck behind another long queue of cars doing 60.

All of this inside an average speed camera section. He must have been doing well over 80 at one point.  

Bonus maths joke:

A mathematician and an physicist agree to a psychological experiment.

The mathematician is put in a chair in a large empty room and a beautiful naked woman is placed on a bed at the other end of the room.

The psychologist explains, "You are to remain in your chair. Every five minutes, I will move your chair to a position halfway between its current location and the woman on the bed."

The mathematician looks at the psychologist in disgust. "What? I'm not going to go through this. You know I'll never reach the bed!" And he gets up and storms out.

The psychologist makes a note on his clipboard and ushers the physicist in.

He explains the situation, and the physicist's eyes light up and he starts drooling. The psychologist is a bit confused. "Don't you realize that you'll never reach her?"

The physicist smiles and replied, "Of course! But in less than half an hour, I'll be close enough for all practical purposes!"

I suspect that pollution may be somewhat improved by the steady flow.  I'm quite happy to have the emotional roller coaster of overtaking whenever possible and racing up the A9 denied me in return for a steady less polluting and reasonably predictable safe journey.

I used to be of the mind set that is now discouraged.  If I want a faster journey overall I just set off very early when there is little traffic

It doesn’t matter if there’s average speed cameras I normally always end up behind someone in a rover with a fish thing on the back and a Panama hat on the parcel shelf check going sensibly along at twenty seven miles an hour.

Thanks for your post and your understanding. And I'm so sorry to hear about the terrible effects of a crash on you and your family

Regarding "idiots who drive recklessly either seem not understand or not to care about the havoc...", I agree with you

Is an average speed camera one which isn't among the best?

as opposed to a top speed camera

They’re not always simultaneous cameras. 

Eg may be the 1st and 3rd, and 2nd and 4th. Depends where entry roads are.  

It's not the cameras, but allowing trucks to do 50mph. This from a local hgv driver. People are more relaxed it they are in a queue at 50 instead of 40 and don't tend to try to overtake.

The whole A9 story has been mainly about traffic speed differentials and these recent changes reduce the differentials even further. A few people are being injured or killed because of confusion over the 3 or 4 types of road layout. Fortunately, a final solution for both the speed differentials and the road type confusion is in play in the form of the dualling programme. 

On the old road (1960s/70s), Inverness to Edinburgh was often 4 hours and still hard work in day traffic. You needed a Triumph TR4 or similar if you wanted to do Edinburgh from Inverness in 2.5 hours or a Lotus 7 Cosworth or 600cc bike to break 2 hours. [GB road deaths were 4 times what they are today and both the A9 and A82 saw some horrendous carnage.]

When the current road was complete, traffic speed differentials were ridiculous, bordering on insane. The constant speed curve design was done like one half of a dual carriageway and had only one decent a straight in 108 miles between Inverness and Perth. Speeds were routinely in the range 35 to 140 mph thus giving a potential speed differential of over 100mph. Eventually, Tayside and Northern traffic cops managed to successfully target those over 100mph, and those driving at 35mph on the basis of what they learned in the 1920s, died off. 

At that stage we had a traffic speed differential reduced to typically 50mph (40 to 90). The crazy stuff was reduced but the road type confusion and sleepy trucker accidents were unaffected. 

With the current regime, most car drivers are between 55 and 65 mph and trucks are doing 56mph against the limiter. So it's not difficult to see how that improves things in terms of the differentials and therefore overtaking accidents. 

So what are the remaining problems? Well, as stated above, the solution is in place for both the speed differentials and the road type confusion. What else? European standards of rest area definitely are required. The Inverness to Perth stretch is particularly needy in this respect but Perth-Dunblane, Perth-Edinburgh and Inverness-Thurso are also problematic. 

Controversially, we are probably about to discover, when A9 dualling is complete, that we should have built a three-lane motorway instead. Oops. That, of course, is on the basis of the 'Field of Dreams' theory of infrastructure development: 'If you build it, he will come'.

But I'm sure the cameras also have an effect. I'd be far more inclined to try to overtake a lorry doing 50, if I could then continue at 70+ rather than 60.

Having spoken to two (yes, two) police officers in the last few months, I have this to add:

The first police officer was a motorcycle speed checker on a stretch of straight road on the Afon Denau in wales, near Tryfan. I asked him about limits and such, and he said that 10%+2 is still correct.

If he's pointing his speed gun at you, and you're doing anything between say 50 and 57, you're probably fine - especially as the speed gun gets effectively instantaneous speed. Note also the speed variation in car speedos mentioned above. 

He can, however, choose to ticket you for going at that speed if he thinks you're driving dangerously. However, if you do 57.1mph according to his speed gun, you *will* be getting a speeding ticket, and he has no choice in the matter.

He said that the same leeway applies to average speed cameras (confirmed by the second police officer), but that speeds between 50 and 57 (in a 50 zone) will be reviewed by someone in an office, and depending on how they're feeling, how much coffee they've had, or whether they notice you've done 56.8mph through that average speed zone eighteen times in the last week, will affect whether you get a ticket.

So I'm just going to set my cruise control to whatever my GPS says is a little over 50 and leave it at that.

With regards the average speed zones on the A9, while it's very dangerous to remain at high speed after the merging of traffic, the first average camera is often over a mile past the end of the dual carriageway, so people can and do get away with it until reaching the first yellow camera.

You seem to have changed your tune a bit since 0955 on Thursday when you said "I deliberately didn't specify whether I meant a time-average <snip> or a distance-average.." and went on to say the correct response to your question was to ask which. 

Check the actual location of the cameras, when they were doing the road works around scotch corner if you joined the A1 from the A66 and travelled northbound there was only one set of cameras, therefore no average speed could be taken, so your average speed wasn’t monitored, regular road users spot things like this and just zoom along.

Of course it is.  I already addressed this in my reply to Robert above, but I'll have one more go.

The requirement to do an average of 30mph overall specifies a time you must take to complete the entire course (lets call it T), and the question requires that you arrive at the halfway point and then make a calculation to work out what speed to travel at for the rest of the journey to make it so. 

The halfway point in distance remains the half way point in distance whether you make the calculation, make it correctly and put your plan into effect or not.  In effect you have free will to make your calculation, correctly or otherwise (the task that is set out for you by the question) and in doing so are not constrained by the initial bounds also set out in the question.

The halfway point in time is only the halfway point in time after the journey is complete, because only then did the entire journey take time T, meaning that half the time had elapsed when you made your calculation at T/2. 

If the halfway point in time was inevitably so at the time that you were there (T/2), there's no point making the calculation, nor making any decision at all as you have no free will at that point and must inevitably arrive at time T whatever you do.  At the time you're making the calculation, the entire journey has in effect already happened.  So the question may as well be phrased in the past tense. 

I gave an example somewhere up there ^ of how Roberts question could have been expressed in the past (and passive) tense, so that it genuinely would have been ambiguous between distance and time.

I've found this interesting to think about, but what definitely *is* now circular is this discussion so I'm out.

My experience is that, like when I'm running/walking/whatever, I naturally tend to maintain a remarkably constant (kinda sorta) 'perceived effort' from throttle position, engine note etc..  Which means in effect slowing down slightly uphill or into a headwind, speeding up downhill or with a tailwind.  It's something I've found only really noticeable by contrast to using cruise control or being governed by a speed limiter when the speed truly is constant and you can feel the 'effort' changing automatically with the conditions to maintain the speed.

The 'musicality' of the individual might make a difference there - I wonder if someone with perfect pitch would naturally drive at constant speed because they're more aware of the absolute 'note' of the engine (and therefore the rpm) than it's timbre (and therefore the power output).  At 70mph, a semitone (eg: the engine note changing from C to C# or vice versa) would be about +/- 3.5mph.

Then: "I deliberately didn't specify.."
Now: "..was not meant to be ambiguous"

Ok, I give up! 

This referred to whether whether a time average or a distance average was intended.

This referred to whether "half way" meant half way in time or in distance.

I think almost everybody will have taken "half way" to refer to distance (as I intended), and assume (very reasonably) that a time average is what is intended, but, with these asumptions, many people then jump to the incorrect answer of 20mph (which would have been correct if a distance average was being calculated).

Are you clear on the difference between a time average and a distance average?

In the end its a spoiler on an interesting maths point and based on present tense semantics (make it past tense and its fine)... exact half distance might also be wrong due to an unexpected diversion further along the road.

Unless I'm missing something, it's very simple. If you know the distance and the average speed required, then it is very simple to calculate half the distance and half the time. eg If total distance is 20 miles and average speed is 40mph, then half the distance is 10 miles and half the time is 15 minutes. What is the issue?

I think I'll just stick to 55 on my speedo

.

Nah on the contrary. I can think of a few roads that would benefit. Sections of the M8 through Glasgow for starters.

Well I think I understand what you mean by that, but if everything you say is correct perhaps not.

I think a 'time average' is the arithmetic mean with respect to time - so, if you plot a graph of speed over time, the 'time average' would be the area beneath the line divided by the time elapsed.  (So a graph of constant "average speed" over the same period - a straight, flat line at the average value, would have the same area underneath it.)

I think a 'distance average' is what you get if you apply to same treatment to a graph of speed with distance travelled on the x-axis instead of time elapsed.

So in a race over a fixed distance (eg: who can cycle a from the start line to the finish line the quickest), the cyclist with the highest time-average speed wins.  In a time-trial (eg: who can cycle the furthest in one hour), it's the cyclist with the highest distance-average speed who wins.

It's reciprocal isn't it?  Time-average speed (eg: miles per hour) equates to distance-average pace (eg: minutes per mile) and vice versa.

Is this correct?**

Ah!

I see what's been going on here.  I was conflating ambiguity between time-average and distance-average with ambiguity between halfway in time and halfway in distance.  (I'm glad now that I didn't really give up.)

What set me off down that rabbit hole was that you did it first and I followed you!  When PaulW asked you whether you meant halfway in time or halfway in distance you talked about time -vs- distance average, and said you "deliberately didn't specify" which.

But of course you did specify - your question could not have been ambiguous in that sense because it concerns average speed cameras that actually exist.  They measure the time elapsed as you travel between fixed points A and B, and therefore are *only* capable of measuring a time average.  If the cameras are 1 mile apart you were speeding if it took less than 2 minutes to travel between them.

You talk about halfway in distance implying the answer is 24mph, halfway in time giving 20mph - in both cases the cameras clock you at a "time average" 30mph.  In the first case the "distance average" is 32mph, in the second it's 33 1/3 mph.

A speed camera that measures a distance average would instead have to follow you for a fixed time and measure the distance travelled - if it tracks you for 2 minutes you were speeding if you travelled more than 1 mile in that time.

In either case the initial conditions - that the camera clocks you at 30mph - require that the whole distance is covered in a certain time and therefore halfway in both time and space are known.  (As above, lets say 1mile and 2mins, so "halfway" might have meant you've travelled for 1/2mile, or for 1min.)  So it seems on the face of it that the question could have been ambiguous about that. 

I see now that you have not, in fact, been arguing that case that it was - that was my mistake. 
(Though Offwidth has, after PaulW hinted at it prompting your erroneous - well, confusing at least - response above.)

My point was that it could not in fact have been ambiguous that way either, because if you're dealing with a real camera (and therefore a time-average) for your question to refer to the halfway point in time would present a paradox involving free-will, pre-destination and such that doesn't arise if it refers to the halfway point in space.

You said above "But the same goes for distance!"  (And Offwidth repeated it in the post above where he accuses me of spoiling your mathematical musings with my philosophical/linguistic/semantic/whatever musings.)

I already tried, twice, at some length to explain how the paradox I'm talking about applied to half-time but not to half-distance with a real speed camera (once in response to you and again in response to Offwidth), and having just written yet another bloody great big essay I'm not going to try to re-phrase it again. 

But I will just mention that the converse is also true.  If you had been talking instead about a distance-average speed camera (one that follows you for 2 mins and issues a ticket if you cover more than 1 mile, say), it would be reasonable to assume that "halfway" in the question means halfway in time and the paradox would instead arise (only) if you meant half way in distance.

Edit to add:
** - I hope it is.  Otherwise everything from this point on is complete gobbledegook!

Sorry about all the gobbledegook.

I thought, immediately, that Robert meant something where the answer was 24 and that john meant something where the answer was 30. 

Correct

Correct

Correct

No, I think the cyclist with the highest time-average wins here too.

To see this you simply need to know that the standard formula S = D/T is always true when S is time average speed, with D total distance and T total time. This is because D = <integral> speed dt = ST

I think this casts into doubt some of what you then go on to say.

Yes, that was the point I was making in my last post.

I agree that it is probably not fair of me to say that my question was deliberately ambiguous whether I measnt time or distance average (as you correctly point out, the cameras can only measure time average (so time average can sensibly be assumed). I should not have gone further than saying that is interesting that the common incoprrect answer of 20mph would have given a dstance average of 30mph.

As for the free will/paradox thing, I'll have to have a think!

You're quite right.  I got carried away looking for symmetries, but of course speed is always the rate of change of distance with respect to time whether it's averaged with respect to time or distance.

I've been thinking about hares and tortoises a bit.  Or two cheetahs and a human runner in a race.

When the starting gun goes off, Cheetah A sprints at 60mph for 30 seconds, then stops to rest for 4.5 minutes before sprinting again.  Cheetah B rests for 4.5 minutes first and then sprints.  The human jogs along at a steady 6mph.  All three can keep this up indefinitely.  The average speed of the human runner (taken over time or distance) is of course 6mph.  The average speed (with respect to time) of both cheetahs fluctuates but tends to 6mph in the long term, their average speed (with respect to distance) remains constant at 60mph.

If the race is over a distance of any multiple of half a mile, or is a time-trial over any multiple of 5mins, it will be a dead-heat between all three.  Over any other distance or time, cheetah A wins, the human comes second, cheetah B comes last.

I don't think so - the free will/paradox thing doesn't rest on that, so remains true (or remains untrue) regardless of my error there, that bit is symmetrical - constrained to travel a certain distance, in choosing a speed you are choosing the time the journey will take.  Constrained to travel for a certain time, choosing the speed instead determines how far you will go.

That isn't a question of mathematics though, so whether you decide to agree or disagree with me having had a bit of a think neither of us gets the luxury of an objectively right or wrong answer.

From personal experience here is how you beat the average speed cameras:

1- if you only pass one camera before you come off at your junction, you can go as fast as you like

2- when you are coming up to a camera, sneak in behind a wagon (really close) so the camera can't see your number plate.

3- (i've not tried this one myself) find a car that looks very similar to yours. make a note of the registration plate. get a new one made, and put it on your car. simples!

Couldn't this be interpreted as speed cameras having reached the peak of their effectiveness, with keeping them in place being a wise thing while other factors are looked at too?

Peak?

Oh they have reached a peak all right. Another peak of ineffectiveness. 

When I first started examining these numbers, the two major factors totalled 56% and had been rising by 1% in most of the previous few years. In the 2017 numbers they were 63%, having floated around the 60 to 70% band for some years (similar period to the flatlining fatality total). 

The Exceeding the Speed Limit factor was 5% in the 2017 numbers, having been 4% in 2014 and floated around 3% to 5% in many of the previous years. 

The basics are that the DfT publishes numbers every year that, in spite of some unhelpful changes in definition and obfuscation of important detail, make it pretty clear what type of road behaviour is most likely to result in death or serious injury. Yet Government policy, infrastructure development, police deployments and court actions often ignore the numbers and obsess instead over a behaviour that has never created the same scale of damage. 

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For a period a few decades ago, numbers like these had been rejected by (some idiot at) the DfT because they were only the subjective opinions of police officers. Eventually, it was noticed that thousands of people were being killed and seriously injured on our roads but we had no idea whatsoever why this was happening. Duh!

We knew that X number of deaths were in Leicestershire or that Y number of deaths were cyclists but causation was a total mystery. So they had to start believing that police officers who had spent years honing their world-class driving skills and picking up bits of people off highways might have something to contribute. In the intervening years, police accident investigation training and operations have been advanced well beyond previous levels. That's why a road near you may have been closed for 5 or 6 hours: so that we can fully understand why somebody who should still be alive is now dead. 

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Now comes the real challenge. Getting politicians to take their heads out of their arses and institute policies that will make a marked difference to road safety. One day before I die I want to open a RRCGB file from GOV.UK and see that the death toll in the previous 12 months is less than 1000. We can do this. It will never happen if we keep obsessing about speeding. 

Keep up the good work Jim.

I may be taking him up on his offer. Last night I was on the M1 on my bike on the managed motorway section close to Chesterfield. I had the cruise control set to 70 and a van over took me (yes it was white). The gantry flashed twice. I checked and my GPS said I was doing 71. The van seemed too far in front for the camera to get him but I feel I was a little too close for the camera on the gantry to get me but I was far enough forward that I saw the flashes in my wing mirror.

So either the zoom on the camera goes further than I thought or I got flashed doing 71 in a 70. Guess I will find out in a week or so if it was me. 

On the plus side I have plenty of evidence that I was only 1mph over, both my sat nav logs the trips and I have a tracker on my bike too. 

I've been flashed, apparently at random, half a dozen times over the last couple of years by the new cameras on the M1 between Sheffield and Leeds.  I wasn't quite sure if I'd just imagined it the first time.  For what it's worth I think it's very unlikely that you have an NIP in the post.

The gantry flashes twice in very quick succession when it catches someone so both flashes might have been for the van?