Combatting lazy uk police with physics formulae

[chunk-uk]

Hello, please could someone help me?

I need to confirm that a physics/maths formula will provide me with the correct data to combat a speeding problem in my road that the local police will do nothing about...

I need to prove that vehicles can accelerate and achieve high speeds within certain distances and then that proof can be used to contradict a senior officers report.

so, I found a maths formula D = Vo x T + 1/2 A x T xT and think that a car will achieve within 5 seconds a distance of 125ft, is that right?
I am using 10 for A ( 10ft/sec/sec ) and half that for motor cycles?

Is there a better way of establishing how far a vehicle travels in a specific time? for example... a Subaru Impreza WRX STi will do 0-60mph in 5.4 secs so how far has it travelled, or a Kawasaki ZX6R j2 does 0-60 in 2.9 secs so how far?
If I can establish a formula to work this out then I can have multiple points at which numerous cars reach 60 mph on our road and it will destroy his argument!

any help gratefully received, I would absoultely love to shove some physics/maths data up his snotty nose, 'cos you just can't argue it.

thanks in anticipation

Steve

 

[Pengwuino]

No, that is the best formula you are going to get. Figure the Subaru's A(cceleration) is 60mph/5.4 seconds. Change that into feet/second^2 , or acceleration, and use that number as you A and plug it in. By the way, motorcycles accelerate much quicker so you probably should have 2x as much A for a motorcycle.

 

[chunk-uk]

this is where I get lost, I was never a very good student! too much rugby and girls !

please could you elucidate further... I am a complete divvy with this stuff, what is ^?

so, I have so far, based on A=10

D= 0x5 +1/2 10 x 5 x 5 = 125ft ( 0 being a standing start )

and you say a bike would be approx half that so 75ft ?? that seems a very short distance to travel and achieve 60 mph?

 

[chunk-uk]

ha ha what a div I am being!

sorry, a bike would do 60mph over 62.5ft, blimey, even shorter!

 

[Pengwuino]

What exactly are you trying ot prove anyways

 

[chunk-uk]

basically our local police inspector has stated that "no vehicle can achieve any great speed in the short distance that our road presents" and has therefore dismissed there being any kind of speeding or reckless driving on our road, hence no further action.

I am a motorcyclist and a high performance car driver and his comments are a crock of sh1t so... I need to prove to the Road Safety Inspector that his comments are fatally flawed.

What I can't do is race the road myself or get mates to do so, so back to formulae

 

[chroot]

A car that can do 0-60 mph in 5.4 seconds is capable of an average acceleration of approximately 5 meters per second squared: http://www.google.com/search?hl=en&lr=&q=60+mph+/+5.4+seconds&btnG=Search

Of course, the car's acceleration is really not a constant 5 m/s^2, but I will assume it.

With such a constant acceleration, the car would cover 72.9 meters in those 5.4 seconds: http://www.google.com/search?hl=en&lr=&q=0.5+*+5+m/s^2+*+(5.4+s)^2&btnG=Search

The motorcycle would achieve 9.25 m/s^2 average acceleration, and would travel approximately 40 meters before reaching 60 mph.

Keep in mind that these numbers can be seriously in error, because neither the car nor motorcycle accelerates uniformly. You would need an acceleration profile (acceleration versus time) for each vehicle to really compute the distances properly.

- Warren

 

[Pengwuino]

How long is the road in question? And nto many people try to push their cars from 0-60 off of a normal road lol

 

[Crosson]

I love the convincing power of physics, but assuming that a car has a constant acceleration from 0-60 mph is not going to convince anyone of anything.

Why don't you just experiment with your own vehicles to see how much distance they cover from 0-60?

 

[brewnog]

Chunk, I appreciate your sentiment any sympathise with you, but Crosson is right. The assumption that a car has constant acceleration isn't going to stand up on its own, let alone in front of a jury.

If I've understood you right, and you need proof that cars are speeding in your area, it would be better to obtain video footage of actual offences being committed.

May I ask which police force you are under? I know it sounds stupid, but it makes a big difference!

 

[Pengwuino]

Oh ok i think i understand what's going on here now...

Yes, you do need video-footage or at least, radar recordings because very few people slam on the gas when they leave an intersection and those 0-60 ratings are most likely with very good gasoline and good tires... something probably 99% of hte public doesn't have. A more convincing argument is getting some midsize economy car to get to speeding-levels in a normal driving manner or a low-priced "sporty" car.

 

[pervect]

Here is one suggestion:

You obviously don't want to make videotape of your car speeding. If you can find an appropriate stretch of highway where it is legal to reach 60 mph, you should be able to demonstrate your point (if is correct) with videocamera and some markers placed at regular intervals by the side of the highway. It may be hard to find a camera angle where you can see at what time the car reaches each marker point clearly, though (overhead would be ideal - and lines across the road would be better than markers at the side). A test track or racing track might also work (you probably don't want to draw lines on public roads).



A video camera with an on-time clock would be the best, ideally the time at which each frame was taken would show up on the frame. With a good vantage point, you could find the exact time at which each marker point was reached, and work out the accleration and (more interestingly) the velocity.

The way the courts work, though, you'd probably be better of finding a lawyer, who would then find an "expert witness" to make your point. This would be $$$ though. Maybe you can find someone who will work pro-bono - if you've got a really solid case, I would hope your lawyer could get court costs back.

 

[chunk-uk]

thanks for all your replies so far...

I'm not trying to get it "judged or juried", just have an argument to hand when confronted with the lazy inspector who has simply dismissed speeding as an issue altogether.

there are too many factors in my particular situation to list here, but

1. the local boy racers do in fact use the road as a standing start raceway to gain speed for the massive hill that faces them, Pengwuino ! it is a 30mph area and top speed achieved on a recent metrocount (police counter) was 76mph ( and there is no speeding problem apparently!)

2. constant acceleration as an assumption is fine because I intend to use manufacturers published 0-60 times for proof of time taken and an approximate distance covered will be enough.

3. we are doing video evidence as well but for the 60mph to 30mph entry point to the village and distance over time will equal speed so my schoolboy physics teacher won the argument that " you will need these lessons in your lifetime"

this turning into a speeding thread, not my intention, apologies, thanks for any formulae provided already, if there are other ways do let me know.

 

[gregmead]

Pervect

why not put the camera inside the car filming out the side window looking at equally spaced markes at the side of the straight road ? Then there would be no paralax error from filming at an angle outside the car.

Then plot the time it takes to travel between each marker, you could then turn that into an acceleration profile for the car.

I think that'd work - correct me if I'm wrong :-)

 

[Kino]

Steve,

this is what I would do first:

Decide on what units to measure in - don't mix metres & feet

Measure the distance involved (call it s feet)

Use the equation v = square root(2 x a x s)

assuming a standing start. Where v = final velocity ft/s
a = acceleration ft/s/s

and draw of graph of v against a. This would give you an indication of what final velocity could be achieved over the fixed distance for a range of accelerations.

You would then have to judge if the acceleration which gives the law-breaking limit over the distance can be achieved by a motor vehicle (car or bike).

Remember to convert mph to fps (feet per second), etc.

Good luck

Here is an example of a table for a distance of 500 ft:

Distance 500 feet
Equivalent to 0 - 60mph
acceleration f/s/s Final velocity f/s mph or 88 fps in
1 31.62 21.56 88.00 seconds
2 44.72 30.49 44.00
3 54.77 37.34 29.33
4 63.25 43.12 22.00
5 70.71 48.21 17.60
6 77.46 52.81 14.67
7 83.67 57.04 12.57
8 89.44 60.98 11.00
9 94.87 64.68 9.78
10 100.00 68.18 8.80

 

[pervect]

thanks for all your replies so far...

I'm not trying to get it "judged or juried", just have an argument to hand when confronted with the lazy inspector who has simply dismissed speeding as an issue altogether.

Well, here is something that might help.

If you can reach a velocity 'v' in a time of t, the absolute theoretidcal maximum distance that it can take you to reach velocity v is v*t.

This assumes a totally unrealisitc near-infinte acceleration to v at t=0. It requires that you accelerate to just under 'v' instantaneously, and then move at that velocity for almost the whole time. You can think of it as accelerating to "just under" v instantaneously, then, at the very end, adding just that little increment of velocity to push you over the top.

If you assume constant acceleration, you can achieve the desired velocity in half that distance.

This may be clearer if you draw a diagram. Remember that distance is the area under the "velocity-time" curve (or equivalently, if you remember your calculus, that distance is the intergal of velocity.

Constant acceleration - velocity vs time

     /
    /
   /
  /
/

Constant velocity (maximum distance) - velocity vs time

-------

The area under the triangle will be 1/2 the area under the square.

This means that if you can go from 0 to 60 miles per hour in 7 seconds, a constant acceleration model will have you reach 60 mph in 308 feet, while the theoretical maximum distance it can take is 60 mph in 616 feet (and this is unrealistically conservative).

If you can find some figures on the maximum acceleration capability of tires, we can probably tighten the theoretical bounds from 2:1 to something lower. Hopefully 2:1 will be good enough.

 

[Danger]

If you can get your mitts on a radar gun, set it up within view of a camcorder aimed at the stretch that concerns you and just leave it for a while. That way you would catch the actual speeders in the act, verified and time-stamped, for use as evidence. You would have to be able to prove that the calibration is accurate, but that shouldn't be too much of a problem.

 

[krab]

thanks for all your replies so far...

I'm not trying to get it "judged or juried", just have an argument to hand when confronted with the lazy inspector who has simply dismissed speeding as an issue altogether.

there are too many factors in my particular situation to list here, but

1. the local boy racers do in fact use the road as a standing start raceway to gain speed for the massive hill that faces them, Pengwuino ! it is a 30mph area and top speed achieved on a recent metrocount (police counter) was 76mph ( and there is no speeding problem apparently!)

Then I don't understand what you need. Since 76mph has already been demonstrated, I would think you have the data you need.

2. constant acceleration as an assumption is fine because I intend to use manufacturers published 0-60 times for proof of time taken and an approximate distance covered will be enough.

Earlier you said you don't know any physics, yet here you show better physics intuition than brewnog and Crosson! To put the assumption on a firmer footing: a motorcycle requires only about 10hp to maintain 60mph. We are talking motorcycles with over 100hp, so the non-constancy of acceleration is at best only a 10% effect. As I understand it, you need only demonstrate that speeds far in excess of 30mph are possible. So you are correct in using the manufacturer's 0-60 times.

 

[brewnog]

Then I don't understand what you need. Since 76mph has already been demonstrated, I would think you have the data you need.

Yeah I was a bit confused by this bit, although I know that it can be impossible (depending on the Constabulary) to have such evidence released, because it's usually used against them.

Chunk, can I just check we all know what you mean? As I've understood it, you're a resident in a 30 zone who is annoyed by boy racers using your road as a drag strip, but the police say they won't do anything about it / dismiss your complaints?

Chunk, what are Metrocounts? The in-car recorders in patrol cars? Or those green radar traps (not cameras) which display your speed on a big sign for everyone to see? The latter are not precise or accurate (or even calibrated), and are often easily fooled, so that would be a no-go.

Earlier you said you don't know any physics, yet here you show better physics intuition than brewnog and Crosson! To put the assumption on a firmer footing: a motorcycle requires only about 10hp to maintain 60mph. We are talking motorcycles with over 100hp, so the non-constancy of acceleration is at best only a 10% effect. As I understand it, you need only demonstrate that speeds far in excess of 30mph are possible. So you are correct in using the manufacturer's 0-60 times.

That's fair enough, but earlier I was under the impression that Chunk was after something which would stand up in court, rather than just provide back-of-envelope figures. If that had been the case (no pun intended... ok, maybe a little!), the officer would have called an expert witness who would have shown that simple calculations don't relate well to real scenarios. Police expert witnesses almost always conclude a case, and the few occasions when they don't require a hell of a lot more than kinematics. But yes krab, you're right.

 

[Pengwuino]

1. the local boy racers do in fact use the road as a standing start raceway to gain speed for the massive hill that faces them, Pengwuino ! it is a 30mph area and top speed achieved on a recent metrocount (police counter) was 76mph ( and there is no speeding problem apparently!)

Well now you finally clarified that its people who are racing that are causing the problems. I am pretty sure we were all under the assumption that you thought people driving along normally were breaking the speed limit.

Best bet is to get video proof of all of this if its that obvious

 

[Danger]

Well now you finally clarified that its people who are racing that are causing the problems. I am pretty sure we were all under the assumption that you thought people driving along normally were breaking the speed limit.

Maybe it's just my background, but the grandstanding was what I read into it from the beginning.

 

[KingNothing]

What is the distance of the road in question? Car-stats.com has graphs of 0-60 speeds according to time, which is what you need and a bit of calculus.

For instance, the Lamborghini Diablo has the following stats:
0-44: 1.5s (30mph)
0-58: 2.0s (40mph)
0-73: 2.7s (50mph)
0-102: 4.6s (70mph)
0-117: 5.8s (80mph)

Please note I rounded down.

To prove a theory incorrect, one must use methods that support it fully, so that there is no argument over manipulating the variables.

In this example, it means assuming that the car instantly accelerates to 44 ft/s for 1.5 seconds. The maximum distance covered is 44*1.5 = 66 feet. THe maximum distance from 44 to 58 is 58*.5 = 29 feet. The maximum distance from 58 to 73 is .7*73 = 51.1 feet. The maximum distance from 73 to 102 is 102*1.9 = 193.8 feet. Final maximum distance = 140.4 feet.

In calculus, this is the same as using the rectangular approximation method to estimate the area under a curve using the right side of the rectangle.

Maximum distance to reach 30mph: 66 feet
Maximum distance to reach 40mph: 95 feet
Maximum distance to reach 50mph: 146.1 feet
Maximum distance to reach 70mph: 339.9 feet
Maximum distance to reach 80mph: 480.3 feet

Please remember these are maximum distances, so the car in reality would have reached those speeds in distances much shorter. If the officer claims no car can reach 40 miles per hour in 95 feet, this proves that the Lamborghini can, for example.

Here is a graph I stole from car-stats.com, and added boxes to shows approximate integrals for the different intervals:

Click here for graph

 

[krab]

Motorcycles, and 4WD cars are limited by the rubber coefficient of friction, which is about 0.9 and means that the acceleration is 0.9 g's (2WD cars cannot reach this because they cannot put all the weight on the drive wheels). This is a=28.8 ft/s^2 (~ agrees with Lamborghini example above: 59ft/s / 2s). What distance required to reach 40 mph (59ft/s)? d=v^2/(2a)=59^2/(2*28.8)=60ft. To maintain 0.9 g's up to 40 mph, need to have sufficient power: calculate Power = F v = W (a/g) v = 550 lbs. (0.9) 59 ft/s = 53 hp. (Motorcycle @ 400 lbs. + rider @ 150 lbs.) Lots of motorcycles have over 53 hp. In summary, a motorcycle needs demonstrate only 2 things: Can break traction in first gear, and > 53 hp. Under these conditions, it can reach 40 mph in 60 ft.

 

[KingNothing]

krab, I have not studied what you said very carefully, but it appears to me that in those equations power is assumed constant? The nominal horsepower of an engine is the peak horsepower. For instance, the nominal horsepower of a chevy 408 crate engine is 408hp, however it does not reach this power until the engine is at about 4700 rpm.

sorry if I am wrong at thinking you kept it constant, i am short on time today.
also, where is weight factored in? a 4000-pound 53hp motorcycle surely will not reach 40mph in 60 feet.

 

[Spin_Network]

Hello, please could someone help me?

I need to confirm that a physics/maths formula will provide me with the correct data to combat a speeding problem in my road that the local police will do nothing about...

I need to prove that vehicles can accelerate and achieve high speeds within certain distances and then that proof can be used to contradict a senior officers report.

so, I found a maths formula D = Vo x T + 1/2 A x T xT and think that a car will achieve within 5 seconds a distance of 125ft, is that right?
I am using 10 for A ( 10ft/sec/sec ) and half that for motor cycles?

Is there a better way of establishing how far a vehicle travels in a specific time? for example... a Subaru Impreza WRX STi will do 0-60mph in 5.4 secs so how far has it travelled, or a Kawasaki ZX6R j2 does 0-60 in 2.9 secs so how far?
If I can establish a formula to work this out then I can have multiple points at which numerous cars reach 60 mph on our road and it will destroy his argument!

any help gratefully received, I would absoultely love to shove some physics/maths data up his snotty nose, 'cos you just can't argue it.

thanks in anticipation

Steve

Allready mentioned by others is the Momentum Factor?..simply explained it goes like this, a hundered cones placed at 1 metre apart

[...................]

a vehicle starting at first cone will attain a specific speed at each consecutive cone -> 5mph ->... thus will take a specific amount of time to attain max speed over certain distance, all pretty standard.

Now if the car allready has a 'max' momentum approaching the first cone, then it will arrive at the next cone, sooner than a 'same' car that does it from a standing start, obvious all vehicles have benchmarked performance figures by manafactures, what cannot be benchmarked is if the owners have 'overclocked' their vehicles to 'outside' the manafacturers 'factory settings'?..you need to test the actual vehicles involved and compile the data with every possible settings, overclocked and standard!

 

[krab]

krab, I have not studied what you said very carefully, but it appears to me that in those equations power is assumed constant?

No, the force is assumed constant. Constant power requires infinite force at zero speed. In straight-line acceleration, constant power is only a good approximation after you've reached redline in first gear. In the mode where you are at the traction limit, the power needed is proportioal to speed; that's why I calculated it at 40mph.

The nominal horsepower of an engine is the peak horsepower. For instance, the nominal horsepower of a chevy 408 crate engine is 408hp, however it does not reach this power until the engine is at about 4700 rpm.

Quite right. Strictly, one needs to find from the gearing what is the rpm at 40mph, and see if the power at that rpm is > 53 hp.

sorry if I am wrong at thinking you kept it constant, i am short on time today.
also, where is weight factored in? a 4000-pound 53hp motorcycle surely will not reach 40mph in 60 feet.

Yes, the weight assumed was 550 pounds.