Any mathematically minded answers?

[SXS]

Taking into account around 1200kg, say there is no excessive wheel spin - excellent starting traction, 4 speed instant solenoid auto-switching box, ratios at:

Gear 1> 3.00:1
Gear 2> 2:1
Gear 3> 1.5:1
Gear 4> 1:1

The drivetrain loss is 10%.

Say you have a drag co-efficient of 0.95:1

13inches of tread on the rear, and 10inches of tread on the front.... Combined unsprung weight of 40lbs per corner...

and say you've got the capability to produce around 950RWHP@7800RPM...

What would be the calculated 0-100mph - 0-150mph - 0-200mph....

Any ideas? I'm sure someone like shpub or other technically minded individuals can show us a formula we can use...

[jsr]

[redacted]

[Martin_S]

To calculate with any sort of reasonable accuracy, you need to feed in a full power curve, so that you can calculate rear wheel thrust (torque)at any given revs and gear.

What is a drag coefficient of 0.95:1?

Drag coefficient is a single figure, not a ratio, and 0.95 would be the proverbial housebrick. A decent modern saloon should be around 0.30 Cd and an open top car like a Griffith or Chimaera is probably around 0.45 - 0.5. Also, drag coefficient is worthless without also knowing the frontal area. Aerodynamic drag is going to be a very major factor is you are calculating acceleration up around 200mph, so a tiny error in frontal area or Cd will lead to a huge error in calculated acceleration times.

Tyre tread and unsprung weights are pretty much irrelevant unless you use a much more sophisticated mathematical model, in which case you will need to feed in a lot more data, such as coefficient of friction for the tyre, diameter of wheel, precise size of contact patch, etc.

There used to be a very simple equation (which I'm afraid I've forgotten) in one of Colin Campbell's old books, just using engine torque, overall weight and a 'bodge factor' that used to give reasonably accurate results for 0-60 and standing 1/4 accelerations, but I'm afraid that anything more advanced than that will require a hell of a lot more data and a very complex mathematical model.

>> Edited by Martin_S on Saturday 9th October 19:02

[SXS]

Yikes, the bible has spoken, thanks MS...

I wander, is there any software out there which you can feed values into and get some form of info out of it... there are a tonne load of formulae out there, I've got a few spreadsheets the engineers have sourced for me, but I want an overall program that I feed variables into and see the calculated results...

anything?

[carl_w]

There is a program called "cartest" which runs in MS-DOS that will calculate these things for you. I got my copy from a site about Sylva cars.

Do a Google for it. If you can't find it, I can zip up and e-mail you a copy. Fortunately, my version already has the standard parameters for a Cerb in it.

For gears, it only has the option of Auto or Manual -- I guess you'd go for Auto (although it may make some assumptions about shift times).

I'll also see if I can put your figures in and get something useful out.

PS: what's going on with your drag coefficient. 0.95:1 is a drag coefficient of 0.95 -- pretty close to the theoretical "barn door"

>> Edited by carl_w on Saturday 9th October 21:17

[carl_w]

OK, I've made some assumptions (around 950 ft/lbs of torque, tubrocharged, standard compression ratio and final drive ratio, 9000 rpm rev limit, standard displacement of around 4.5 litres, Cd of 0.31-ish) and got the following:

0-60 2.1
0-100 6.4
standing 1/4 10.6 at 136.5 mph
top speed 199 mph (looks rev limited rather than drag-limited to me)

Didn't really arse around with the wheels and tyres, so assumed standard 16s.

I don't know how accurate this is, but it seems pretty close for a very wide range of cars.

[GreenV8S]

Could that 0.95 be CdA rather than Cd? Bit high but not unreasonable.

[Martin_S]

carl_w said:

OK, I've made some assumptions (around 950 ft/lbs of torque, tubrocharged, standard compression ratio and final drive ratio, 9000 rpm rev limit, standard displacement of around 4.5 litres, Cd of 0.31-ish) and got the following: 0-60 2.1 0-100 6.4 standing 1/4 10.6 at 136.5 mph top speed 199 mph (looks rev limited rather ftthan drag-limited to me) Didn't really arse around with the wheels and tyres, so assumed standard 16s. I don't know how accurate this is, but it seems pretty close for a very wide range of cars.

Fcuk me!! 950lb-ft of torque!!?? What are you planning to fit, a Rolls Royce Merlin?!

Edited to add...no ignore me, a Merlin would go bang at about 3,500 revs, never mind 9000!

I know you are probably just Trolling, but go on, you've intrigued me - what exactly are you planning?!

>> Edited by Martin_S on Saturday 9th October 21:55

[GreenV8S]

carl_w said:

0-60 2.1 0-100 6.4

Is this assuming infinite traction? I reckon you need to *average* 1.3G to get 0-60 in 2.1, which implies Mu of about 2 to achieve this with rear wheel drive and a realistic weight distribution. Of course it is all academic, but these figures do seem a bit optimistic!

Edited to add: incidentally SXS, I haven't registered with your web site (because I don't like sites that insist on registering their visitors) but it sounds as if you've got a real fun project there.
Have you worked out what gearing you will need in order to be able to put that much torque down without smoking the wheels? I suspect you'll strugle to put it down in anything except fifth, and even that may be too low!

>> Edited by GreenV8S on Saturday 9th October 22:02

[SXS]

Hmmm, so how come a few stock drag cars with 750bhp at the wheels are pulling 1/4 ETs in the 8-9 second region, and they weigh around 2000kg too?

I dont agree with the numbers posted above at all...
You'd have to drop the compression ratio considerably for a 4.5 with say a bpfs bore:91mm / stroke:86mm... no way in hell you could push that much torque with standard cr...

anyway..

GreenV8s,

Sorry about the logging in part, its all to keep the traffic down, and anyone who is interested in the project will sign up and give a few pointers here and there hopefully, usually keeps the odd browser out of the site anyway... hehe...

If you did sign-up, you would have seen the Stage 2 post which goes into detail of hopefully how all that torque will be mated with the ground...

>> Edited by SXS  on Saturday 9th October 22:10

[Martin_S]

At risk of butting in on GreenV8S's answer:

1) a stock drag car weighing 2000 kg? Really?! That's the sort of weight you'd expect from a fully loaded top of the range Merc or Bentley limo. not something that's been prepped for drag racing, surely? ...not that I have the slightest clue about drag racing, I must admit, but the sort of acceleration figures you are quoting are serious stuff!

2) Drag cars use some pretty serious tricks to get exceptional traction and particularly favourable weight distribution.

None of your figures make any sort of sense to me, which seriously intrigues me.

I can't get into the website linked from your profile, registration or not - it just comes up with an error on my browser. Go on, give us a precis of the project you have in mind and it might all become a whole lot clearer!?

[jsr]

This is more complicated than i expected. It's tough enough working with an assumption of constant torque, but this doesn't give a very good result (obviously).

To get a more accurate answer, you need the equation of the torque curve, which leads to some extremely complex integration.

I need to find another approach for my model, as currently i would have to do the integration for each car i want to use in my simulator (over 50 at present), and i also wanted users to be able to input their own vehicle data to compare with pre-programmed cars, which will be almost impossible this way.

Essentially the formula is f = ma , the net force being the torque at the wheels less rolling resistance less drag. The problem is that to get any kind of accuracy involves really complex maths.

Think i might take a break tomorrow and actually drive my car instead

[Martin_S]

jsr said:

This is more complicated than i expected. It's tough enough working with an assumption of constant torque, but this doesn't give a very good result (obviously). To get a more accurate answer, you need the equation of the torque curve, which leads to some extremely complex integration. I need to find another approach for my model, as currently i would have to do the integration for each car i want to use in my simulator (over 50 at present), and i also wanted users to be able to input their own vehicle data to compare with pre-programmed cars, which will be almost impossible this way. Essentially the formula is f = ma , the net force being the torque at the wheels less rolling resistance less drag. The problem is that to get any kind of accuracy involves really complex maths. Think i might take a break tomorrow and actually drive my car instead

Yep, this analysis of the problem is pretty much spot on...a basic rule of thumb is that actually calculating what your car is likely to do is always at least 15 times more complicated than actually building the thing and testing it!

[carl_w]

Well give me some numbers and I'll plug 'em in. I need to know the following:

Engine
Displacement
Location (front/rear/mid)
Type (NA/Supercharged/Turbocharged/Sequential)
BHP x at y rpm
Torque x at y rpm

Drivetrain
No of transmission speeds
Type auto or manual
Gear ratios and final drive
Driving wheels

Chassis and body
Weight
% weight on front wheels
Wheelbase
Tyre section width (go for the largest -- it's used to calculate frontal area)
Wheel diameter
Drag coefficient
Overall height
Overall width
Ground clearance

[SXS]

If its an all out drag car - then they're light as feck, but some of the hardcore yanks have produced road going cars that hit the strips and have slips with 8-9 sec prints... anyway, this is irrelevant...

the question remains, whats e=mc2 for cars?

jsr - I would love to see your software in action... any beta previews of it? I've got some figures that I could possibly pump through...?

[jsr]

Engine
Displacement : 4.0 litre
Location (front/rear/mid) : f
Type (NA/Supercharged/Turbocharged/Sequential) : na
BHP x at y rpm : 214 @ 5785
Torque x at y rpm : 213.7 lb ft

Drivetrain
No of transmission speeds : 5
Type auto or manual : m
Gear ratios and final drive : 2.95, 1.95, 1.34, 1.0, 0.73, final 3.31
Driving wheels : rear

Chassis and body
Weight 1165kg
% weight on front wheels : 51%
Wheelbase 2282mm
Tyre section width (go for the largest -- it's used to calculate frontal area) : 225
Wheel diameter : 16"
Drag coefficient : 0.34
Overall height : 1215mm
Overall width : 1865mm
Ground clearance : ? 120mm

My model gave a result of 5.8 secs for 0-60mph. I've recorded 5.6 in real life and strongly believe it's ultimate time could be 4.9-5.0 secs, so my model needs a bit of tweaking.

The biggest assumption so far is using constant torque of 90% of the maximum torque - though i do actually get 90% of my torque from 2000rpm to 5700rpm.

[jsr]

sxs - no simulation as yet. I've only a not very accurate formula for speed in terms of time. Once it becomes more accurate, i'll then need to get distance in terms of time, then i can make the simulation.

Here is my current quarter mile sim. It's based on real performance data (ie. o-10,20,30, etc). It's pretty accurate in visual terms, but you get some crazy results if you try to measure data from the formulas used. That's why there are no speeds of times displayed.

[carl_w]

OK, for jsr I get (with a launch method optimized for 0-60 time: 3200 rpm dumping the clutch):

0-60 5.9
0-100 14.4
standing quarter 14.4 @ 99.9 mph
flat out at 143

PS: You didn't specify the RPM at which the peak torque was developed -- I guessed at 5600. Nor the tyre profile -- I guessed at 50%. Nor the compression ratio and rev limit -- I took the figures from a standard Chimaera at 8.9:1 and 6500 rpm.

>> Edited by carl_w on Saturday 9th October 23:33

[SXS]

Carl, can you work backwards?

Say we want a 0-100mph in 5 secs
and a 0-200mph in 15 secs

what spec do you come up with to achieve that? with a V8 bored and stroked to 6000cc...
and anything else you want to do to it...

[docevi1]

This is a co-incidence, this is my dissertation work for this year at Uni.