Not building related maths question

[Russdl]

I’ve just been on one of those course you are invited to take instead of 3 points on your driving licence (I was innocent! So were the other 20 people on the course). 
 

One element of the course explained that with two identical cars, one doing 30 mph one doing 31 mph braking at exactly the same time the car doing 30mph would stop at point ‘X’. The car doing 31 mph would still be doing 8 mph at point ‘X’. 
 

I couldn’t argue that because I don’t know where to start on the maths. Can one of you boffins show me the ‘workings’ of such a sum?

 

 

[ProDave]

I look forward to the answer.  It sounds more like "this is what you should think"

 

I suspect on those courses it is futile to argue you are right and they are wrong.  It's a case of "yes sir of course sir" biting your tongue if needed.

 

[joe90]

5 minutes ago, ProDave said:

I look forward to the answer.  It sounds more like "this is what you should think"

 

I suspect on those courses it is futile to argue you are right and they are wrong.  It's a case of "yes sir of course sir" biting your tongue if needed.

 

+1, your either too close or not 🤷‍♂️ (braking distances in the Highway Code are way out of date .)

[garrymartin]

No AI's were harmed during this answer... 😉

 

[saveasteading]

5 minutes ago, ProDave said:

biting your tongue if needed

Been there, learnt my lesson. So good I'm doing it again next week.

 

60,000 miles since the last time, shows that I'm a good person really......is not the sort of thing to say.

 

Yes, people argue pointlessly. Sit still. Answer the most glaringly obvious questions with the 'correct' answer.

Watch the taxi driver.....he says as little as possible.

 

At 8mph the remaining stopping distance is going to be, apparently 12 ft. by extrapolating the attached.

[Adrian Walker]

8 mph sounds about right, but I would need to do the maths. That’s why just going a bit faster, which you and the others weren’t, makes a huge difference. 

[Russdl]

@garrymartin I got lost in the maths there but it would seem they were telling truths. 
 

They weren’t talking about stopping distances per se more about how fast you would still be going at the point the ‘compliant’ car had stopped. I was quite surprised. 
 

What about the speed of a car at point ‘X’ if it’s doing 35 mph, that’ll be significant I suspect? 
 

it sounds like I’m a convert but it is my second course so they haven’t fixed me yet 😔

[garrymartin]

7 minutes ago, Russdl said:

What about the speed of a car at point ‘X’ if it’s doing 35 mph, that’ll be significant I suspect?

18 mph apparently.

[joe90]

This presumes both cars have the same tyres, correct pressure etc etc, I think it’s a bit presumptuous. I have only rear ended a car once when I was 17, the brakes failed (it was an old banger) so I must be doing something right. I have done a speeding awareness course, Road I knew well and I knew that around the bend was a 30mm limit, well there was a copper with a speed gun and I had a smile on my face, TILL I got a speeding notice a week later, they changed the speed limit to 20 mph but my periphery vision did not pick up the change 🤷‍♂️. 

Edited September 27 by joe90

[MikeSharp01]

I guess whichever way you look at it the limit is the limit not the target and the sums also work to tell you that you will be stopped from 29 mph when the 30 mph car is still going.  

[Gus Potter]

1 hour ago, garrymartin said:

No AI's were harmed during this answer...

I hope not!

 

1 hour ago, Russdl said:

I’ve just been on one of those course you are invited to take instead of 3 points on your driving licence (I was innocent! So were the other 20 people on the course). 

Of course.. voluntary work is so good for the soul.

 

Ok the maths. I'll relate this to wind load on a house then cut to the chase about driving at hwich I'm a bit not Nigel Masell.. more like Rowan Atchinson.. enough knowledge to be dangerous but without the cash to excecute well.  Excuse the spelling and grammer please.

 

Simplistically the wind load on a house is related to the speed of the wind as we know for life experience. The general equation is air mass x  the wind speed squared. For interest ( if you have nothing beter to do) I've screen shotted a wind diagram from the BS design code.

 

 

 

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For the non mathematical often we can simplify maths by removing things that stay the same.. say the weight of your car. This lets us quickly compare like with like even though the number we get at the end does not equate to say a true real life value that we could then use to design a roof truss say. We can call this a qualitative analysis.

 

In Oxford the basic wind speed is 20 metres per second... about 45 miles per hour (gust speed).. Build Hubbers.. do not use this as a value for your design.. as it then gets modified a lot. In the North of the country it is say 27 - 31 metres per second. Using the equation..  force =  mass x velocity squared the two results can be compared in a qualitative manner. That said I hope the wind diagram helps you see how things could change for your house design depending on where you live. If you have big areas of glass then its a consideration.. is the glass and double glazing going to be ok if I live in Cornwall say.

 

The mass of air is the same (except in the far north and the Hebrides where it is rarified by Whisky fumes so is a little lighter) so the "Energy ~ = mass of air * wind velocity squared.  Just say the mass of air is 1.0 something units

 

1.0 * 20^2 = 1.0 * 20 *20 = 400 units.

 

In the North it's 1.0 * 27^2 = 1.0 * 27 *27 = 729 units.. nearly double the force! When explaining to other designers about wind behavoir I often use the car velocity / breaking distances model as an example as most folk can relate to it.

 

If you hit a kid when driving at 20 mph the energy you hit them with is similar to the wind. Your car = say 0.75 - 2 tonnes.. but it's the velocity that causes a lot of damage. Say your car weights 1.0 unit of measure.

 

At 20 mph the qualitative units are mass of your car  1.0 * 20 * 20 = 400 units.

 

At 30 mph it mass 1.0 * 30 * 30 = 900 units. In other words that extra 10 mph matters a lot. The extra 10 mph has more than double the energy.

 

Now it's known that the survival rate for humans rapidly decreases when the intensity of the energy delivery increases if you get hit by something. This is what we call accelerating or braking if you are in the car. When folk go to the moon they get accelerated by a rocket but slowly.

 

Now the driving courses are intended to make sure you stop before you hit anything.. as a kid could then get slowly rolled over by the wheels of you car at 1 -2 mph. The main thing about the above it to recognise that with a small increase in speed you need to exponentially decrease the rate of acceleration. To be frank.. if you hit someone at a couple of miles an hour you are unlikey to cause them organ damage. But as above the collateral damage comes from then running them over with your car or causing them to fall over and then damage their head say from the fall.

 

Now if you are in an airplane.. the guy / doll up front has a big interest in not crashing at any time! At 150 - 300 knots a bit of difference in relative ground speed is not going to make any difference to you not getting squished. The last thing they are wanting to do is to make contact with anything solid or semi solid in the air.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[ProDave]

Today I had a refresher of just how quick you can stop.  I was doing barely 10mph rounding the corner of a junction making a left turn when two schoolkids stepped out in front of me without looking.  I was impressed with just how quick the car stopped, my reactions were still quick, the front of the car dipped considerably with the rapid braking and I am sure the stopping distance was just a couple of feet, and all without locking the wheels.

 

The thing about all these 20mph limits is they are in effect saying to drivers, we don't think you have the ability to make your own decision and drive to a safe speed for road conditions.  That I find insulting.  Yes along the high street of the town when there are lots of people about, crossing the road between parked cars because they are too lazy to use the crossings it makes perfect sense to drive slow.  But the other end of the town one of the estates has a feeder road like a big ring.  There are massive wide grass verges both sides before the actual roads with the houses and it is rare to see anybody walking along or crossing this feeder road, yet still it has a 20 limit now where it is rare to see a pedestrian.

 

I am just glad I don't live in Wales.

[Russdl]

2 hours ago, garrymartin said:

18 mph apparently.

That, I guess, was the point they were trying to make. It resonated with me, especially the 1 mph extra resulting in 8 mph extra at point ‘X’ which could be where the car/bike/person etc is. 
 

I was baffled by the 1 mph becoming 8 mph so thanks @garrymartin for confirming that bit of weirdness is a reality. 

[Gus Potter]

4 minutes ago, Russdl said:

It resonated with me

That makes sense. I presented the maths but your reaction time is slow so yes you will probably not stop and still hit folk with enough force to hurt them.

[nod]

You have my sympathy I’ve been on two of these corses 

Two hours of my life I’ll never get back 

[Russdl]

26 minutes ago, ProDave said:

But the other end of the town one of the estates has a feeder road like a big ring.  There are massive wide grass verges both sides before the actual roads with the houses and it is rare to see anybody walking along or crossing this feeder road, yet still it has a 20 limit now where it is rare to see a pedestrian.

I was snapped as a 3 lane 40 mph limit expanded to a 4 lane 30 mph limit.

 

Definitely no pedestrians or even footpath close by. I was doing 34 mph, I didn’t see the 30 mph sign. Too much street furniture?

 

Or maybe I wasn’t paying enough attention, either way nothing but my pride and wallet were hurt and who knows this thread may may slow some down by 1 mph or more and prevent a them hitting a car/bike/person in a future scenario. 
 

I’m not preaching here, I have a Speed Triple that doesn’t really do ‘slow’ very well. 

[joe90]

39 minutes ago, Russdl said:

I have a Speed Triple that doesn’t really do ‘slow’ very well. 

I get that, whilst I tend to “potter” in my car I find it difficult to potter on my Moto Guzzi 🏍️

[Gus Potter]

I've got a Seat Ibiza... that I use for my SE surveys... and it goes like stink to my surprise. I thought it was a run around.. I've never looked under the bonnet and it just looked like a wee small car when I bought it. Can't understand why it goes faster than I expect. 

 

Wife has the posh car and it goes a bit faster and that car seems to be a points magnet.

Edited September 27 by Gus Potter

[Russdl]

42 minutes ago, Gus Potter said:

Wife has the posh car and it goes a bit faster

Isn’t that always the way!

[Gus Potter]

But I love her to bits and she is my sole mate.

 

Anyway my wee car just looks like a standard car to me. Kwick fit said it might have be "modified" I think they were referring to the sound system.. I'm an old raver and like old school techo music.. the sounds are great.. like the frosties ad. Sometimes Techno music helps my creativity as an SE, other times classical music.

 

Very happy for my best pal to have the posh car. I do worry how much it will cost if I prang my wee car.. but "we buy any car.com" don't put much value on it anyway.

 

 

[SteamyTea]

It is to do with energy, 1/2 mass times velocity squared.

So the bigger the difference in initial speed, the greater the amount of energy to dissipate.

Then there is wind resistance, which works in your favour at higher speeds, the faster you go, the greater the resistance, (air resistance = air density x drag x area / 2) x velocity squared.

Then there is aerodynamic forces that affect the vehicle, most cars produce lift at the rear end, this gets worse the faster you go.

Then, just for a laugh, there is the braking forces, which changes the axle weigh (remember that weight is mass times acceleration).  As you brake hard, more force is put on the front axle, which causes a greater force on the tyres, which then deform, increasing the contact area.  Now at normal speeds, this does not make any difference as friction is just the coefficient times the force, but at high speeds, it does as the tyres can quickly change shape (ripple).

 

As a general rule, if your driving goes Pete Tong, in any situation, hit the brakes as hard as possible, it scrubs of speeds, lowering the energy on impact (I went backwards into a tyre wall at over 90 MPH at Thruxton, was airborne and the steering and brakes did (expletive deleted) all, did not stop me trying to use them).

 

13 hours ago, saveasteading said:

Been there, learnt my lesson. So good I'm doing it again next week.

 

60,000 miles since the last time, shows that I'm a good person really

I last got caught in 2002, was doing 94 on the A11 near Snetterton.  They are usually used to tractors throwing carrots out the back.

£270 fine and 5 points.  Failed to turn up in court as I was working in the USA, so kept my licence (apparently to be banned you had to appear, or be represented, in court).

So in the last 22 years, I have probably driven 700,000 miles.  I drive like my Mother, but that is another story.

 

Yesterday I drove 600 miles, got 68 MPG and my average speed was 51 MPH.  That is 12 hours of my life I am never getting back.