Computer simulation of vehicle performance
Discussion
Pumaracing said:
Luv a duck Stan. No wonder I had such a job trying to work out what you'd done. This may however deserve some sort of award for the most errrm "creative" juggling with the variables in a simulation to try and match a set of bum speeds and times ever seen.
As to real gear change times with manual boxes, look at the data Stevieturbo posted. You can see the width of the gaps in the acceleration curve at each change and it's about 0.5 seconds from power off to fully back on again. However some acceleration is still taking place as the tyres and clutch grip again so the total time lost is a bit less than this.
From simulations over the years checking car magazine road tests I reckon the best a professional test driver can do is about 0.25 to 0.3 seconds when it's not his own car and he doesn't care about breaking anything. It's not easy for an owner to be quite so brutal.
From datalogs, I'd say on average my shifts with the synchro box would be around 0.5s from on-off-on throttle againAs to real gear change times with manual boxes, look at the data Stevieturbo posted. You can see the width of the gaps in the acceleration curve at each change and it's about 0.5 seconds from power off to fully back on again. However some acceleration is still taking place as the tyres and clutch grip again so the total time lost is a bit less than this.
From simulations over the years checking car magazine road tests I reckon the best a professional test driver can do is about 0.25 to 0.3 seconds when it's not his own car and he doesn't care about breaking anything. It's not easy for an owner to be quite so brutal.
With the dog style box and no lift, no clutch, total cut time can be around 200-220ms. ( actual shift takes less but that's total power reduction including shift time )
I'm sure some better synchro boxes would allow down to the 3-400ms range though, the T56 is hardly renowned as a slick shifter though
A friends Samsonas sequential would be quicker again, actual shift average taking around 60-65ms, how long you apply power cut to enable the shift would be up to you, but could easily see a total of 150ms or so
Nissan GTR's with their dual clutch setup are even faster again.
I recall my mate in an F1 team telling me about the new seamless shift boxes that were coming in 7 or 8 years ago. It wasn't just that the change time was down to about 15 ms or so, maybe even less now, but somehow you actually gained a little kick of power by utilising the inertia of one gear cluster that was already spinning up but not yet engaged as another cluster disengaged.
It was all very hush hush and he couldn't go into details but I doubt it would have been comprehensible to mere mortals anyway. I have enough trouble remembering how a normal gearbox works.
The one thing I never built into my simulation which does have a small effect on very high speed vehicles is the loss of speed during the gear change which then has to be made up again. You can see about 2 mph on your own car on the 4th to 5th change.
It was all very hush hush and he couldn't go into details but I doubt it would have been comprehensible to mere mortals anyway. I have enough trouble remembering how a normal gearbox works.
The one thing I never built into my simulation which does have a small effect on very high speed vehicles is the loss of speed during the gear change which then has to be made up again. You can see about 2 mph on your own car on the 4th to 5th change.
I do not know what to say about the shift times as I have never measured them. I do know that I have shifted stock synchro boxes (GM Muncie 4 speed, BW T10 4 speed and Tremec 5 speed that did have a Pro 5.0 shifter) using the clutch but never lifting the gas peddle from the floor.
Stan
Stan
Stanley,
I have a little exercise for you. When an engine revs at full throttle in neutral the power is being absorbed solely by the engine's own internal component inertia. By timing the rate of increase in rpm from idle to rev limiter it should be possible to exactly calculate the shape of the entire torque curve.
With a known engine bhp the rotating inertia should be calculable or vice versa.
I assume that these ecu data loggers might be able to time the rpm increase. I'm struggling with the maths to program the power curve though. Reckon you can crack it?
I have a little exercise for you. When an engine revs at full throttle in neutral the power is being absorbed solely by the engine's own internal component inertia. By timing the rate of increase in rpm from idle to rev limiter it should be possible to exactly calculate the shape of the entire torque curve.
With a known engine bhp the rotating inertia should be calculable or vice versa.
I assume that these ecu data loggers might be able to time the rpm increase. I'm struggling with the maths to program the power curve though. Reckon you can crack it?
Pumaracing said:
Stanley,
I have a little exercise for you. When an engine revs at full throttle in neutral the power is being absorbed solely by the engine's own internal component inertia. By timing the rate of increase in rpm from idle to rev limiter it should be possible to exactly calculate the shape of the entire torque curve.
With a known engine bhp the rotating inertia should be calculable or vice versa.
I assume that these ecu data loggers might be able to time the rpm increase. I'm struggling with the maths to program the power curve though. Reckon you can crack it?
The datalog could easily record that, but obviously it would only apply to n/a enginesI have a little exercise for you. When an engine revs at full throttle in neutral the power is being absorbed solely by the engine's own internal component inertia. By timing the rate of increase in rpm from idle to rev limiter it should be possible to exactly calculate the shape of the entire torque curve.
With a known engine bhp the rotating inertia should be calculable or vice versa.
I assume that these ecu data loggers might be able to time the rpm increase. I'm struggling with the maths to program the power curve though. Reckon you can crack it?
Well I've come up with an answer Stan although my head is hurting so I'm not 100% sure it's correct. By my calculations an engine producing 100 ft lbs of torque ought to be able to accelerate an inertia mass of 25 lbs at an average radius of gyration of 3.5 inches at about 14,500 rpm per second.
In other words to go from 1000 rpm to 6500 rpm should be about 0.4 seconds.
Does that look right to you?
In other words to go from 1000 rpm to 6500 rpm should be about 0.4 seconds.
Does that look right to you?
Pumaracing said:
Well I've come up with an answer Stan although my head is hurting so I'm not 100% sure it's correct. By my calculations an engine producing 100 ft lbs of torque ought to be able to accelerate an inertia mass of 25 lbs at an average radius of gyration of 3.5 inches at about 14,500 rpm per second.
In other words to go from 1000 rpm to 6500 rpm should be about 0.4 seconds.
Does that look right to you?
Dave ,In other words to go from 1000 rpm to 6500 rpm should be about 0.4 seconds.
Does that look right to you?
I took the easy /lazy way out with my time increment.
; RPM Time
ROad HP = 1000 0.0
ROad HP = 1500 0.04
ROad HP = 2000 0.08
ROad HP = 2500 0.12
ROad HP = 3000 0.16
ROad HP = 3500 0.20
ROad HP = 4000 0.24
ROad HP = 4500 0.28
ROad HP = 5000 0.32
ROad HP = 5500 0.36
ROad HP = 6000 0.40
ROad HP = 6500 0.44
which is 12500 PRM per second
Stan
The numbers run together because I did not program the printout for that large of an accelerate rate.
Road Horse Power Prediction Chart.
These numbers will be similar to a Chassis Dyno.
Rear Aero Rolling Rear W Accele Time Rate
RPM MPH Velocity Wheel dynamic Resist. Elapsed Horse ration Differ RPM
ft/sec Torque Drag - HP HP Time Power in G's ential Sec
1000.0 20.825 30.543 0.00 .000 .000 .0000 0.00 0.0000 0.0000 0.0
1500.0 31.237 45.815 86.53 .000 .000 .0400 24.71 11.8664 0.0400 12500.0
2000.0 41.650 61.087 86.53 .000 .000 .0800 32.95 11.8664 0.0400 12500.0
2500.0 52.062 76.358 86.53 .000 .000 .1200 41.19 11.8664 0.0400 12500.0
3000.0 62.475 91.630 86.53 .000 .000 .1600 49.42 11.8664 0.0400 12500.0
3500.0 72.887 106.901 86.53 .000 .000 .2000 57.66 11.8664 0.0400 12500.0
4000.0 83.300 122.173 86.53 .000 .000 .2400 65.90 11.8664 0.0400 12500.0
4500.0 93.712 137.445 86.53 .000 .000 .2800 74.14 11.8664 0.0400 12500.0
5000.0 104.125 152.716 86.53 .000 .000 .3200 82.37 11.8664 0.0400 12500.0
5500.0 114.537 167.988 86.53 .000 .000 .3600 90.61 11.8664 0.0400 12500.0
6000.0 124.950 183.260 86.53 .000 .000 .4000 98.85 11.8664 0.0400 12500.0
6500.0 135.362 198.531 86.53 .000 .000 .4400 107.09 11.8664 0.0400 12500.0
Averages 86.53 65.90 0.0400 12500.0
PS - Edited the output so the numbers did not run together.
Edited by Stan Weiss on Tuesday 23 June 15:33
OK I created a new time line.
ROad HP = 1000 0.0
ROad HP = 1500 0.0343
ROad HP = 2000 0.0686
ROad HP = 2500 0.1029
ROad HP = 3000 0.1372
ROad HP = 3500 0.1715
ROad HP = 4000 0.2058
ROad HP = 4500 0.2401
ROad HP = 5000 0.2744
ROad HP = 5500 0.3087
ROad HP = 6000 0.343
ROad HP = 6500 0.3773
Stan
ROad HP = 1000 0.0
ROad HP = 1500 0.0343
ROad HP = 2000 0.0686
ROad HP = 2500 0.1029
ROad HP = 3000 0.1372
ROad HP = 3500 0.1715
ROad HP = 4000 0.2058
ROad HP = 4500 0.2401
ROad HP = 5000 0.2744
ROad HP = 5500 0.3087
ROad HP = 6000 0.343
ROad HP = 6500 0.3773
Stan
Road Horse Power Prediction Chart.
These numbers will be similar to a Chassis Dyno.
Rear Aero Rolling Rear W Accele Time Rate
RPM MPH Velocity Wheel dynamic Resist. Elapsed Horse ration Differ RPM
ft/sec Torque Drag - HP HP Time Power in G's ential Sec
1000.0 20.825 30.543 0.00 .000 .000 .0000 0.00 0.0000 0.0000 0.0
1500.0 31.237 45.815 100.90 .000 .000 .0343 28.82 13.8384 0.0343 14577.3
2000.0 41.650 61.087 100.90 .000 .000 .0686 38.43 13.8384 0.0343 14577.3
2500.0 52.062 76.358 100.90 .000 .000 .1029 48.03 13.8384 0.0343 14577.3
3000.0 62.475 91.630 100.90 .000 .000 .1372 57.64 13.8384 0.0343 14577.3
3500.0 72.887 106.901 100.90 .000 .000 .1715 67.24 13.8384 0.0343 14577.3
4000.0 83.300 122.173 100.90 .000 .000 .2058 76.85 13.8384 0.0343 14577.3
4500.0 93.712 137.445 100.90 .000 .000 .2401 86.46 13.8384 0.0343 14577.3
5000.0 104.125 152.716 100.90 .000 .000 .2744 96.06 13.8384 0.0343 14577.3
5500.0 114.537 167.988 100.90 .000 .000 .3087 105.67 13.8384 0.0343 14577.3
6000.0 124.950 183.260 100.90 .000 .000 .3430 115.28 13.8384 0.0343 14577.3
6500.0 135.362 198.531 100.90 .000 .000 .3773 124.88 13.8384 0.0343 14577.3
Averages 100.90 76.85 0.0343 14577.3
Excellent. I agree your calculations exactly at 0.3773 seconds with 100.9 ft lbs.
So now all we need is some data from people with ecu logging capability of engine acceleration rate from idle upwards to red line with engines of roughly known power curves. Then we can calculate the engine inertia properly.
So now all we need is some data from people with ecu logging capability of engine acceleration rate from idle upwards to red line with engines of roughly known power curves. Then we can calculate the engine inertia properly.
Nice website with Javascript calculators for wheel, tyre and engine inertia.
http://hpwizard.com/rotational-inertia.html
http://hpwizard.com/rotational-inertia.html
I tried a little experiment with my own car, 2.0 litre Ford Focus 130 bhp, this morning. Blipping the throttle and timing the rpm increase with a stopwatch. As near as I could measure 1000-6000 rpm was 1.1s and 2000-6000 was 0.78s.
I know the power curve pretty exactly both from manufacturer figures and also rolling road tests.
I exactly match the above times with a total inertia of 85 lbs at 3.5" radius but that's far too high. If I put that number in a simulation the car is about 1 second too slow in the 1/4 and correspondingly everywhere else. It matches road test data with the 25 lb inertia figure I settled on many years ago after many simulations of different cars.
So I'm back to square one. Is there something about revving the engine when the car is stationary that prevents the rpm from rising as fast as just inertia would dictate? Maybe the rate at which inlet maniflow airflow can keep up with throttle demand or summat?
I know the power curve pretty exactly both from manufacturer figures and also rolling road tests.
I exactly match the above times with a total inertia of 85 lbs at 3.5" radius but that's far too high. If I put that number in a simulation the car is about 1 second too slow in the 1/4 and correspondingly everywhere else. It matches road test data with the 25 lb inertia figure I settled on many years ago after many simulations of different cars.
So I'm back to square one. Is there something about revving the engine when the car is stationary that prevents the rpm from rising as fast as just inertia would dictate? Maybe the rate at which inlet maniflow airflow can keep up with throttle demand or summat?
Pumaracing said:
I tried a little experiment with my own car, 2.0 litre Ford Focus 130 bhp, this morning. Blipping the throttle and timing the rpm increase with a stopwatch. As near as I could measure 1000-6000 rpm was 1.1s and 2000-6000 was 0.78s.
I know the power curve pretty exactly both from manufacturer figures and also rolling road tests.
I exactly match the above times with a total inertia of 85 lbs at 3.5" radius but that's far too high. If I put that number in a simulation the car is about 1 second too slow in the 1/4 and correspondingly everywhere else. It matches road test data with the 25 lb inertia figure I settled on many years ago after many simulations of different cars.
So I'm back to square one. Is there something about revving the engine when the car is stationary that prevents the rpm from rising as fast as just inertia would dictate? Maybe the rate at which inlet maniflow airflow can keep up with throttle demand or summat?
Dave,I know the power curve pretty exactly both from manufacturer figures and also rolling road tests.
I exactly match the above times with a total inertia of 85 lbs at 3.5" radius but that's far too high. If I put that number in a simulation the car is about 1 second too slow in the 1/4 and correspondingly everywhere else. It matches road test data with the 25 lb inertia figure I settled on many years ago after many simulations of different cars.
So I'm back to square one. Is there something about revving the engine when the car is stationary that prevents the rpm from rising as fast as just inertia would dictate? Maybe the rate at which inlet maniflow airflow can keep up with throttle demand or summat?
How would those time change if you removed the accessory drive belt from the engine?
Since 1000-6000 was 1.1x and 2000-6000 was 0.78s 1000-2000 was 0.32 plus. Maybe try 3000-6000?
Stan
Stan Weiss said:
Dave,
How would those time change if you removed the accessory drive belt from the engine?Stan
Dunno Stan. That would involve, oh what are those things called?, ah, "tools" and getting my hands dirty. Not my thing at all.How would those time change if you removed the accessory drive belt from the engine?Stan
However if the accessory drive belt is taking a load equivalent to 60 lbs of inertia at 3.5" radius then it would snap like an elastic band.
Pumaracing said:
Dunno Stan. That would involve, oh what are those things called?, ah, "tools" and getting my hands dirty. Not my thing at all.
However if the accessory drive belt is taking a load equivalent to 60 lbs of inertia at 3.5" radius then it would snap like an elastic band.
Dave,However if the accessory drive belt is taking a load equivalent to 60 lbs of inertia at 3.5" radius then it would snap like an elastic band.
Where did that number come from? This is 25 lbs at 3.5"s.
Road Horse Power Prediction Chart.
These numbers will be similar to a Chassis Dyno.
Rear Aero Rolling Rear W Accele Time Rate
RPM MPH Velocity Wheel dynamic Resist. Elapsed Horse ration Differ RPM
ft/sec Torque Drag - HP HP Time Power in G's ential Sec
1000.0 20.825 30.543 0.00 .000 .000 .0000 0.00 0.0000 0.0000 0.0
2000.0 41.650 61.087 21.63 .000 .000 .3200 8.24 2.9666 0.3200 3125.0
3000.0 62.475 91.630 35.50 .000 .000 .5150 20.28 4.8683 0.1950 5128.2
4000.0 83.300 122.173 35.50 .000 .000 .7100 27.04 4.8683 0.1950 5128.2
5000.0 104.125 152.716 35.50 .000 .000 .9050 33.79 4.8683 0.1950 5128.2
6000.0 124.950 183.260 35.50 .000 .000 1.1000 40.55 4.8683 0.1950 5128.2
Averages 32.72 25.98 0.2200 4727.6
Stan
Stan, here is the flywheel power curve from my car off a Dastek chassis dyno. Rated power is 130 bhp so spot on. I had to guesstimate the rpms below 1500.
500...8.5
1000..18.0
1500..29.0
2000..44.3
2500..58.4
3000..68.9
3500..84.4
4000..97.2
4500..106.7
5000..122.9
5500..129.0
6000..126.0
I match the 2000 rpm to 6000 rpm time of 0.78s with 87 lbs at 3.5" inertia.
So about 60 lbs more than I usually use for a 4 pot engine of 25 lbs. No way it's really as high as 87 lbs.
500...8.5
1000..18.0
1500..29.0
2000..44.3
2500..58.4
3000..68.9
3500..84.4
4000..97.2
4500..106.7
5000..122.9
5500..129.0
6000..126.0
I match the 2000 rpm to 6000 rpm time of 0.78s with 87 lbs at 3.5" inertia.
So about 60 lbs more than I usually use for a 4 pot engine of 25 lbs. No way it's really as high as 87 lbs.
I just had a good play with the inertia calculation website I linked above.
I weighed the wheels and tyres off my Focus. 205/50/16 tyres with a rolling radius of 0.963 feet.
Tyre weighed 8.8 kg. Total was 17.3 kg so 8.5 kg for the wheel.
The website gave me an equivalent total inertia mass (including the base weight) of 16.9 kg for the tyre and 11.6 kg for the wheel so a total of 28.5 kg. That's 65% higher than the base weight of 17.3 kg and as I posted somewhere above my own rough calculations many years ago had come up with about 3/4 of the base weight as being the add on for inertia effects. So pretty close.
So I've been adding about 125 lbs for wheel/tyre inertia to my simulations and this more accurate calculation would indicate 17.3 x 4 x 65% = 45 kg or 99 lbs for those sized tyres. Maybe a tad more once brake disc, hub, driveshafts are added in.
From now on I'll stick to 100 lbs for the average family car though and increase or reduce that for different vehicles. However a few lbs one way or the other on a 3000 lb vehicle are neither here nor there so I've been within 1% all along.
I weighed the wheels and tyres off my Focus. 205/50/16 tyres with a rolling radius of 0.963 feet.
Tyre weighed 8.8 kg. Total was 17.3 kg so 8.5 kg for the wheel.
The website gave me an equivalent total inertia mass (including the base weight) of 16.9 kg for the tyre and 11.6 kg for the wheel so a total of 28.5 kg. That's 65% higher than the base weight of 17.3 kg and as I posted somewhere above my own rough calculations many years ago had come up with about 3/4 of the base weight as being the add on for inertia effects. So pretty close.
So I've been adding about 125 lbs for wheel/tyre inertia to my simulations and this more accurate calculation would indicate 17.3 x 4 x 65% = 45 kg or 99 lbs for those sized tyres. Maybe a tad more once brake disc, hub, driveshafts are added in.
From now on I'll stick to 100 lbs for the average family car though and increase or reduce that for different vehicles. However a few lbs one way or the other on a 3000 lb vehicle are neither here nor there so I've been within 1% all along.
Dave
Notice how the acceleration rate varies and follows the torque curve. 25 lbs 3.5 inches
Also notice the anomaly at 5000 RPM or is it 4500 rpm?
Stan
Notice how the acceleration rate varies and follows the torque curve. 25 lbs 3.5 inches
Also notice the anomaly at 5000 RPM or is it 4500 rpm?
Stan
Road Horse Power Prediction Chart.
These numbers will be similar to a Chassis Dyno.
Rear Aero Rolling Rear W Accele Time Rate
RPM MPH Velocity Wheel dynamic Resist. Elapsed Horse ration Differ RPM
ft/sec Torque Drag - HP HP Time Power in G's ential Sec
1.0 .021 .031 0.00 .000 .000 .0000 0.00 0.0000 0.0000 0.0
500.0 10.412 15.272 89.72 .000 .000 .0385 8.54 12.3044 0.0385 12961.4
1000.0 20.825 30.543 94.82 .000 .000 .0750 18.05 13.0043 0.0365 13698.6
1500.0 31.237 45.815 100.32 .000 .000 .1095 28.65 13.7582 0.0345 14492.8
2000.0 41.650 61.087 115.37 .000 .000 .1395 43.93 15.8219 0.0300 16666.7
2500.0 52.062 76.358 123.17 .000 .000 .1676 58.63 16.8917 0.0281 17793.6
3000.0 62.475 91.630 119.76 .000 .000 .1965 68.41 16.4241 0.0289 17301.0
3500.0 72.887 106.901 126.78 .000 .000 .2238 84.49 17.3867 0.0273 18315.0
4000.0 83.300 122.173 127.24 .000 .000 .2510 96.91 17.4506 0.0272 18382.4
4500.0 93.712 137.445 124.72 .000 .000 .2787 106.86 17.1047 0.0278 18018.0
5000.0 104.125 152.716 129.14 .000 .000 .3055 122.95 17.7111 0.0268 18656.7
5500.0 114.537 167.988 122.95 .000 .000 .3337 128.76 16.8617 0.0282 17762.0
6000.0 124.950 183.260 110.22 .000 .000 .3651 125.92 15.1165 0.0314 15923.6
Averages 115.35 74.34 0.0304 16664.3
Edited by Stan Weiss on Wednesday 24th June 16:28
Some more tyre weights from my collection of crap in the garage. This should cover a fair chunk of the car market for inertia calculation purposes.
195/50/15 - 7.4 kg
205/50/16 - 8.8 kg
225/60/16 - 11.2 kg
225/45/17 - 11.2 kg
Interestingly there's an almost perfect cube law relationship between the section width and the weight. Scaling the 100 lbs add-on calculated above for the 8.8 kg 205 tyre would give 84 lbs and 127 lbs for the other two weights.
195/50/15 - 7.4 kg
205/50/16 - 8.8 kg
225/60/16 - 11.2 kg
225/45/17 - 11.2 kg
Interestingly there's an almost perfect cube law relationship between the section width and the weight. Scaling the 100 lbs add-on calculated above for the 8.8 kg 205 tyre would give 84 lbs and 127 lbs for the other two weights.
Pumaracing said:
Some more tyre weights from my collection of crap in the garage. This should cover a fair chunk of the car market for inertia calculation purposes.
195/50/15 - 7.4 kg
205/50/16 - 8.8 kg
225/60/16 - 11.2 kg
225/45/17 - 11.2 kg
Interestingly there's an almost perfect cube law relationship between the section width and the weight. Scaling the 100 lbs add-on calculated above for the 8.8 kg 205 tyre would give 84 lbs and 127 lbs for the other two weights.
Dave,195/50/15 - 7.4 kg
205/50/16 - 8.8 kg
225/60/16 - 11.2 kg
225/45/17 - 11.2 kg
Interestingly there's an almost perfect cube law relationship between the section width and the weight. Scaling the 100 lbs add-on calculated above for the 8.8 kg 205 tyre would give 84 lbs and 127 lbs for the other two weights.
Switching back and forth between kg and pound. What will you post next? Maybe a mixed metaphor or an oxymoron.
Stan
PS - It is tire.
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