Question for the math heads
Discussion
Total time from green light to finish line = RT + ET. So Andy was 4.210s, Stig was 4.222s. Thus there was a 0.012s difference between them at the line. Once Andy's already crossed the line, we're interested in how far behind Stig was at that point. He averaged 459km/h over the last 66 feet (he'll probably have been doing slightly more than that at the finish line, but we can't measure that, so we'll use the average). So in 0.012s at 459km/h, you'll travel 1.53m, which is a good approximation of the margin of victory.
Dominic, Tet has pretty much summed it up, but to expand slightly on his post:
As there are so many variables concerning the speed (Is either driver slowing or still accelerating ?, Which speed do you use ?, etc) it is generally accepted that the average of the 2 speeds is used to give the best approximate distance between the vehicles at the line. I do it this way, as do the NHRA.
I have a spreadsheet that works it out in feet, inches and mm; happy to send it over if you pm an email address.
As there are so many variables concerning the speed (Is either driver slowing or still accelerating ?, Which speed do you use ?, etc) it is generally accepted that the average of the 2 speeds is used to give the best approximate distance between the vehicles at the line. I do it this way, as do the NHRA.
I have a spreadsheet that works it out in feet, inches and mm; happy to send it over if you pm an email address.
crikey said:
it is generally accepted that the average of the 2 speeds is used to give the best approximate distance between the vehicles at the line. I do it this way, as do the NHRA.
I still maintain that averaging the speeds is a mistake, as the speed of the winning vehicle has no bearing on the margin of victory[1]. But in general, it'll work reasonably well for close run races under full power, which is by and large the only time you care about MOV. And ultimately, no matter which method you use, it's all an approximation anyway. Which method is better can only really be settled with high speed cameras at the finish line...[1] Depending, of course, on how you define the MOV.
Tet said:
crikey said:
it is generally accepted that the average of the 2 speeds is used to give the best approximate distance between the vehicles at the line. I do it this way, as do the NHRA.
I still maintain that averaging the speeds is a mistake, as the speed of the winning vehicle has no bearing on the margin of victory[1]. But in general, it'll work reasonably well for close run races under full power, which is by and large the only time you care about MOV. And ultimately, no matter which method you use, it's all an approximation anyway. Which method is better can only really be settled with high speed cameras at the finish line...[1] Depending, of course, on how you define the MOV.
MOV needn't be about races under full power, what about a slowing vehicle being pipped at the line for example. I know you said "by and large" but it's a good example of another variable.
With so many variables an average is the only sensible option, and as I said, it's the best approximation.
Tet said:
I still maintain that averaging the speeds is a mistake, as the speed of the winning vehicle has no bearing on the margin of victory[1]
...
[1] Depending, of course, on how you define the MOV.
Exactly. Is it how far behind the other car was when the winner crossed the line or is it how far in front was the winning car when the losing car reached the line? Worded like that then option 1 is the only option that makes any sense but I am sure someone could eloquently argue for the other side....
[1] Depending, of course, on how you define the MOV.
For an extreme example imagine a bracket race between a tractor with a top speed of 26mph and a doorslammer with a top speed of 100mph, both going at a steady speed through the speed trap. For the purposes of this calculation the tractor got there first by 0.01 seconds and they had identical reaction times.
So, using option 1:
Distance = Speed x Time
= 100mph x 0.1 seconds
= 4.47m
So when the tractor crossed the line the doorslammer was 4.47m behind
Using option 2:
26mph x 0.1 seconds
= 1.16m
So when the doorslammer crossed the line the tractor was only 1.16 metres ahead
Quite a difference really. Using the averaging method:
(100+26)/2 x 0.1 seconds
= 2.82m
Which represents an arbitrary point in time after the tractor crossed the line but before the doorslammer crossed the line.
All of this is probably far more than you wanted to know but you did ask!
TIP: If you don't like converting your units use Google:
http://www.google.co.uk/search?hl=en&q=(100mph...
Time Machine said:
a lot of technical gubbins
Which in the situation whereby one car was closing on another leads to the interesting question "How much longer would the racetrack need to be before I beat him?This needs to use Option 1 where we have fixed numbers of 4.47 meters and a speed difference of 74mph,
Time = Distance / Speed
= 4.47m / 74mph
= 0.135 seconds
This gives us the time difference. Putting this into another calculation, this time just for the tractor (as it was in front):
Distance = Speed x Time
= 26mph x 0.135 seconds
= 1.57 metres
All of which only applies to vehicles at a steady velocity. The maths gets far too confusing after that, though I am sure some people would love to extrapolate a 990ft race to 1320 using an approximating model to see if there are races which would have had a different outcome had they been completed to the stripe (oooh, controversial :-))
Apologies if my maths is wrong btw, it has been a long time since I stretched that part of my brain in any way whatsoever.
The vehicle slowing scenario is not likely to be as extreme as the tractor example you've used Martin, but it is quite likely in bracket racing as we know from the amount of times brake lights are seen at the finish line. That was the point I was trying to make, I perhaps just didn't make it very well 
crikey said:
The vehicle slowing scenario is not likely to be as extreme as the tractor example you've used Martin, but it is quite likely in bracket racing as we know from the amount of times brake lights are seen at the finish line. That was the point I was trying to make, I perhaps just didn't make it very well
No, I got the point and just couldn't resist rambling on about it :-)The average seems a good compromise for information purposes, the inner geek in me would love to see so many data points from the timing system you could do all sorts with it - imagine a continuous line of timing cells so you get about 1 every foot. You'd get through a lot of foam blocks when the Altereds come out though, and I probably just gave you nightmares...
Great comment from Time Machine concerning 'How much longer would the track need to be'. I remember when Steve Clark was helping your dad out with a Rover powered altered, Steve explained that 'had the track been twenty feet longer we'd have beaten him' - I think it was Dave Wilson who said 'Steve, if it ran on all eight you'd have p*ssed it'. Happy days.
fester426 said:
Martin,,your dad was in here at the weekend ,he said that he had aquired a computer for the new car,,he said you would be pleased,,,,,,,,,,,now i understand why!! ........bill
Yeah, I'll admit I can get stuck into numbers. It's a late 80's / early 90's Racepack so fits the Nostalgia theme, should get it to play with soon :-)MrExile said:
Great comment from Time Machine concerning 'How much longer would the track need to be'. I remember when Steve Clark was helping your dad out with a Rover powered altered, Steve explained that 'had the track been twenty feet longer we'd have beaten him' - I think it was Dave Wilson who said 'Steve, if it ran on all eight you'd have p*ssed it'. Happy days.
That Rover was pretty much my introduction to the sport, tidy little car but had a tendency to eat itself - something to do with the big blue bottle. I was only on polishing detail so it can't have been my fault :-)
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