Computer simulation of vehicle performance

[Pumaracing]

Hi Stan,

We seem to have some differences in the results of our computer simulations based on the same data. Perhaps it might help both of us if we run some simplified test data through our programs and make sure we both have the correct algorithms.

I've designed a very basic simulation data pack with most of the bells and whistles eliminated for now. We can put them back in later.

Engine torque 200 ft lbs everywhere from idle to 6000 rpm (rev limit)
No transmission losses so above are essentially wheel figures
Tyre radius 1.000 ft
A single gear of total ratio 2.5 (28.559 mph/1000 rpm)
Mass 3000 lbs (no rotational inertia for now re wheels or engine components)
Frontal area 22 sq ft
Cd 0.33
Rolling resistance 0.013

What do you get for times and speeds for 20, 220, 440, 880, 1760 yards. What is the top speed and at what rpm?

[Pumaracing]

Stan Weiss said:

Hi Dave,
Slow day, or you just want to pick on the poor yank? Not sure how your software works but I get 28.57143 mph/1000 rpm

Hmmm. I was hoping to agree on the basic maths bits at the very least.

1000 x 60 / 2.5 x 2 x pi / 5280 = 28.55993

Maybe check your value for pi or there's some rounding error going on.

Stan Weiss said:

I am using a 1 ft roll out

If it matters I have the Track BP = 29.92126

60 Foot ET = 4.1562
330 Foot ET = 10.7970
1/8 Mile ET = 15.6822
1/8 Mile MPH = 52.3750
1000 Foot ET = 19.5965
1/4 Mile ET = 22.7513
1/4 Mile MPH = 73.1093

1/2 Mile ET = 33.193 -- 1/2 Mile MPH = 98.02
1 Mile ET = 49.225 -- 1 Mile MPH = 124.48
2 Mile ET = 75.520 -- 2 Mile MPH = 145.97

Ok we have some strangeness going on. I agree your top speed of 157 mph so within narrow limits we agree on the aero and rolling drag. Your ETs are quite different though at the bottom end of the range.

60 Foot ET = 4.93 @ 16.6
330 Foot ET = 11.61 @ 38.4
1/8 Mile ET = 16.51
1/8 Mile MPH = 53.4
1/4 Mile ET = 23.58
1/4 Mile MPH = 73.4

1/2 Mile ET = 34.03 -- 1/2 Mile MPH = 98.0
1 Mile ET = 50.06 -- 1 Mile MPH = 124.4
2 Mile ET = 76.35 -- 2 Mile MPH = 145.9

Take out the "rollout" whatever that is and just launch the car instantaneously at 200 ft lbs. However I suspect this will just increase the differences though. You should find the car launches at 0.1537 G.

Wheel force = 200 x 2.5 = 500
rolling resistance = 0.013 x 3000 = 39
Net force = 461
Accel = 461/3000 = 0.1537 G

You appear to be accelerating initially much faster than this which is impossible.

Just using the simple Newtonian equation S = ut + 0.5at^2 :-->

Distance = 60 ft = 18.288m

Accel = 0.1537 x 9.80665 = 1.5073 m/s^2

t^2 = 18.288 / 1.5073 x 2 = 24.27

t = 4.93 - as my program calculates.

Sort your way through that lot and hopefully some booboo will show up in the programming.

[Pumaracing]

OK, the times are now right at the bottom end but the speeds are still wrong and as they are both functions of the same acceleration curve I don't see how that is possible.

There must be another offset in the program somewhere which is reducing the speeds. I wonder.... On a real 1/4 mile track the speeds are worked out as the average over some distance leading up to each marker rather than an instantaneous speed at distance. Is that what's built in perhaps?

[Pumaracing]

Now for some of the bells and whistles. A big factor in a real car is the rotating / reciprocating inertia.

1) Wheel and tyre mass
2) Crankshaft, flywheel, pistons

Without these factors built in to the equations a low powered, i.e. non grip limited, car will accelerate drastically differently to the correct model, especially in the low gears and most particularly if the engine is high revving and therefore high geared.

To give you an example of my own 2 litre Ford Focus which is not particularly high revving and therefore nowhere near the worst case scenario, the inertia in first gear is equivalent to an additional 1/4 of the base vehicle mass.

On a friend's high revving motorbike engined hillclimb single seater the inertia in 1st is equivalent to an additional 50% of the base vehicle mass! i.e. it soaks up 1/3 of the engine's horsepower.

How does your program account correctly for these?

[Pumaracing]

I think it's actually 20 yards not feet, at least at the 1/4 mile point and for the particular track I found data for online many years ago. It may well vary with different types of timing equipment and certainly it can't be the average over 20 yards for the 60 foot point or the number would be about half the true speed and therefore meaningless.

Anyway I don't think that's the problem in Stan's calcs because his speeds have proportionally different discrepancies at different distance points. His speed now at 220 yards of 52.31 mph (should be 53.4 mph) appears to be the speed actually pertaining at 210 yards but his speed of 73.02 mph at 440 yards (should be 73.4 mph) is not the true speed for 430 yards, it's actually about the true speed at 435 yards.

Anyway, I'm sure he'll find it.

[Pumaracing]

Stan Weiss said:

How do you handle the difference in HP based on the type of dyno test done?
Steady state test or acceleration rate of xxx RPM /Second each of these will show a different HP for the same engine.

Only steady state numbers are true bhp as far as I'm concerned. I don't mess about trying to adjust for anything else.

What about rotational inertia?

[Pumaracing]

Stan Weiss said:

1/8 mile is 600 ft + 660 ft mph's / 2

1/4 mile is 1290 ft + 1320 ft mph's / 2

OK, good. So as I calculated above, at 210 yards and 435 yards effectively.

Despite us no doubt using very different programs and methods we have now agreed the full time and speed curve calculations from a given power curve and vehicle mass without rotational inertia factored in so that's a good start.

If you do ever want to get into inertia calculations I can help with the equations for different gears and the sort of numbers to input for different engine types.

[Pumaracing]

That's not something I've ever programmed Stan.

[Pumaracing]

Ok, seeing as it was only a five minute job to add a speed squared dependent Bernoulli equation to the torque curve I stuck it in the program to have a look see.

60 Foot ET = 4.93 @ 16.56
330 Foot ET = 11.61 @ 38.38
1/8 Mile ET = 16.50
1/8 Mile MPH = 53.49
1/4 Mile ET = 23.57
1/4 Mile MPH = 73.50

1 Mile ET = 49.94 -- 1 Mile MPH = 125.24
2 Mile ET = 76.00 -- 2 Mile MPH = 147.53
3 Mile ET = 99.68 -- 3 Mile MPH = 155.31
4 Mile ET = 122.60 -- 4 Mile MPH = 158.21
5 Mile ET = 145.25 -- 5 Mile MPH = 159.25

Top speed 160 mph

So yeah, you got the equations right.

[Pumaracing]

Stan Weiss said:

Dave,
Great. Maybe you help me out then. Over the years I have fine tuned my logic a few times. When using normal air density it is fine. I believe when using lower air densities I any coming up low.

Air Density is 0.076501 @ 160 MPH = 1.0309367 increase

Air Density is 0.060000 @ 160 MPH = 1.0242638 increase - Shouldn't I still get the same 1.0309367 increase?

Nah mate. Ram effect is 1/2 x air density x MPH^2 so the effect will always rise and fall with barometric pressure.

However as the air density changes so obviously do both the aero drag and also the engine bhp so the acceleration curve will be affected by both.

Aero drag in lbs at STP is CdA x V^2 x 0.00256 but as air density alters so will that 0.00256 number. As air density falls so will engine power and ram effect.

Anyway I can't be arsed with all this stuff in my own program. It just assumes STP.

Edited by Pumaracing on Tuesday 16th June 00:51

[Pumaracing]

stevesingo said:

Dave/Stan,


60 Foot ET 2.89
330 Foot ET 6.61
1/8 Mile ET 9.55
1/8 Mile MPH 85mph
1000 Foot ET 12.02
1/4 Mile ET 14.06
1/4 Mile MPH 111.7mph

This is not an internally consistent set of data and hence not possible to simulate. A car of that weight hitting 85 mph at 220 yards should only be doing about 105 mph at 440.

Alternatively if it really hits 111.7 at 440 yards it should be doing about 91 mph at 220 and hitting the 1/4 mile in 13.3 seconds.

I'll have to pass because the variability of the power figures necessary to juggle different parts of that acceleration curve correct is so high as to leave almost zero confidence in the results. Either these are not good numbers or the track grip was massively different in different places or the engine power kept changing.

And Stan! Oi! No you didn't get a consistent simulation out of that set of numbers. It isn't possible.

[Pumaracing]

stevieturbo said:

In a couple of months if everything hangs together, I'd hope it will run around 185mph in the 1/2 mile pushing 190-200mph over 1km.
I think 200mph is a bit much to ask, but based on last year I've no doubt 190+ is achievable over standing 1km, as long as 5th gear survives.

All very interesting stuff. I'd never have believed such simulations would/could mirror reality.

To hit 185 mph at 1/2 mile you'll need about 1060 flywheel bhp and kilometre will be 195.8 mph

To hit 200 mph in the kilometre you'll need 1130 bhp. 1/2 mile will be 189 mph.

That assumes your slicks and 1.8g off the line. On road tyres you'll be several mph off those numbers.

Reality is just physics. Computers do physics rather nicely if the programming is correct. My program is now so complex after 25 years of adding bells and whistles to it I daren't tinker with it much further in case it achieves sentience and decides it no longer needs me.

One day the machines will rise!

[Pumaracing]

On road tyres at 0.6g off the line you'll need 1230 bhp to hit 200 mph at 1 km.

1/2 mile will be 187 mph.

[Pumaracing]

ivanhoew said:

so chaps , is it the case that if one has a very traction limited fwd car , then drag run data is not going to allow a good sim ? i wonder if this means a sim of my turbo mini would be unviable?robert.

No. The traction can be any value at all as long as it's consistent. The simulation allows for it by taking the 60 ft time.

[Pumaracing]

Stan Weiss said:

Steve,
OK, it is hard to simulate this run. Using no roll out I get

60 Foot ET = 3.0525
330 Foot ET = 6.7346
1/8 Mile ET = 9.5686
1/8 Mile MPH = 86.9256
1000 Foot ET = 12.0068
1/4 Mile ET = 14.0533
1/4 Mile MPH = 110.8472

using around 242 RWHP

Stan

Sorry Stan but you're miles out. We know the basic maths in both programs agree but something is going wrong when more complex car details are entered. If you aren't allowing for engine inertia and wheel/tyre inertia then the bhp numbers are always going to be too low.

[Pumaracing]

stevesingo said:

Dave/Stan,

Can you do the calc for the following…

RWD
1300kg
0.33Cd
1.88m2 frontal area
CdA 0.62

1st 3.72
2nd 2.40
3rd 1.77
4th 1.26
5th 1:1
Final drive 3.15

225/45 R16 tyre

60 Foot ET 2.89
330 Foot ET 6.61
1/8 Mile ET 9.55
1/8 Mile MPH 85mph
1000 Foot ET 12.02
1/4 Mile ET 14.06
1/4 Mile MPH 111.7mph

OK, I've had another crack at it after a night's sleep. It was quite tricky. I think there was a bit of wheel spin off the line which means the track grip and 60 ft ET is not really quite as bad as it looks so I've factored that in. I still can't quite agree the 1/8 mile speed but the rest has matched quite nicely.

60 Foot ET 2.83
330 Foot ET 6.65
1/8 Mile ET 9.56
1/8 Mile MPH 87.2mph
1000 Foot ET 11.99
1/4 Mile ET 14.03
1/4 Mile MPH 111.7mph

Flywheel bhp is 340. Wheel bhp is 289.

[Pumaracing]

Ivanhoew - just to make sure, your vehicle weight does include the driver I take it?

[Pumaracing]

Ok Ivanhoew

Another quite tricky run to simulate compared to Stevieturbo's but I get a reasonable match at about 213 flywheel bhp, 180 ish at the wheels.

[Pumaracing]

stevieturbo said:

Would a lazy launch, getting into say 3, 4, 5th quicker and using more torque as opposed to rpm's to achieve the speed work better than launching and going as hard as possible the entire way.

No. You're confusing two different things. Saving a gearchange between two specific speeds might well be a good idea but over a whole run you have to change into every gear anyway. You can't go quicker by doing this earlier than usual. You want to maximise engine power delivered at all times.

With low grip tyres, if your clutch is up to it, then what you want to do is launch in 2nd or even 3rd because you're just spinning away power in 1st.

[Pumaracing]

So what did the dyno say?