Vxt 0-60 In 1.7s?!

My physics is a bit rusty, and I know cars are not very efficient machines, but surely they are not only 12% efficient at converting power at the wheels into acceleration? Someone who knows what they are doing please correct me...

Source

could be in completely over my head here but are there not a lot of other factors that need to be considered like wind resistance, drag etc. maybe it would do it in 1.7-in space! have no idea, just thought i'd share my thoughts!

i'll test my understanding of all this and see if i can drag some stuff up from my Mechanical Engineering degree I would guess the biggest losses are going to be in things like the gearbox, differential and other mechnical resistance (bearings etc). 1.7 seconds 0-60 would not be possible because a lack of grip anyway, but iirc gearboxes are only about 90% efficient. I know that high efficiency gearbox is 98% efficient, so there is a 2% loss at least. If you are only looking for a 12% loss overall to justify the actual acceleration figures i think this is where they will be. The differential is effetively a simple gearbox, so that will loose at least 2% as well. I am sure one of the car designer types on here will know for sure! It is hard work trying to trawl my mind for the things that were said when i was sitting through my lectures. I have to say i wasn't the least bit interested in them. I spent most of my time chatting up 'Angie', the only fit girl in the lecture theatre of 80 people. Have to say i had a fair bit of success with her too Anyway enough reminiscing, back to the real world. Jim

Edited by jimgraham, 16 August 2005 - 07:53 AM.

Also, you're calculation assumes the engine makes peak power at all revs. The revs will be somewhere between 3500 and 6500 rpm for 1st and 2nd gears, so the average power figure will be lower. A quick check of a power curve will confirm this. You'd also need to factor in the time lost during gearchanges.

i'll test my understanding of all this and see if i can drag some stuff up from my Mechanical Engineering degree

I would guess the biggest losses are going to be in things like the gearbox, differential and other mechnical resistance (bearings etc). 1.7 seconds 0-60 would not be possible because a lack of grip anyway, but iirc gearboxes are only about 90% efficient. I know that high efficiency gearbox is 98% efficient, so there is a 2% loss at least. If you are only looking for a 12% loss overall to justify the actual acceleration figures i think this is where they will be. The differential is effetively a simple gearbox, so that will loose at least 2% as well. I am sure one of the car designer types on here will know for sure!

It is hard work trying to trawl my mind for the things that were said when i was sitting through my lectures. I have to say i wasn't the least bit interested in them. I spent most of my time chatting up 'Angie', the only fit girl in the lecture theatre of 80 people. Have to say i had a fair bit of success with her too

Anyway enough reminiscing, back to the real world.



Jim

Jim, firstly my bhp figures are "at the wheel", which should include loses at the gearbox etc...

Secondly, the 12% I quoted is a percentage of power at the wheels being converted to acceleration - my maths is saying that only 57bhp of the 147bhp in an NA is converted into accelerating the car, the rest of it is lost somewhere...


... unless my maths is flawed, which i'm assuming it is...

Gary - maybe you've got it there... if I integrated the bhp curve and took an average, maybe it would be nearer that 57bhp?

Secondly, the 12% I quoted is a percentage of power at the wheels being converted to acceleration - my maths is saying that only 57bhp of the 147bhp in an NA is converted into accelerating the car, the rest of it is lost somewhere...
nearer that 57bhp?

fair enough!

like i said i was rusty (and had noticed only half of the facts!!)

Still from what your saying, I am not sure why only 12% of the power at the wheels is converted into acceleration (is this right??), or how 12% of 147hp is 57hp .

I think your right though, Gary might just have the answer!



Jim

Edited by jimgraham, 16 August 2005 - 08:59 AM.

First a lot of energy is lost in the gearbox, tyres etc. Maybe 120 HP is available @wheels. Secondly, this power is not available when you drop the clutch in 2000 rpm. Then you might have only 50 HP or so. So you should calculate with a mean power from where you "shift till where you shift".

The exercise that you are trying to perform is almost impossible using theory alone. It may well be fair enough to assume a 12-14% loss throught the transmission in order to assume a power at the wheels at any given speed, though torque at the wheels is a more useful quantity really. From the torque figure you can work out the maximum tractive force that the vehicle can apply to the road at any given speed by dividing the torque at the wheel by the tyre outside radius. (As a small caveat here the modelling of tyre deformation and hysteresis is unbelievably complex and the sums never really come out right so typically you use empirical techniques to model such things, which I'll get to). Newton tells us that every action has an equal and opposite reaction if it's state is to remain the same. The vehicle clearly accelerates so the force supplied by the engine is clearly greater than the forces trying to resist the motion of the vehicle. These are typically modelled using a widely accepted Road Load Simulation equation: Fl = k0 + k1.v+k2.v.v + m.g.sin(theta) Where: Fl is the total losses in newtons k0 is the 'stiction' loss in newtons k1 is the coefficient for losses proportional to speed (typically bearing and transmission) k2 is the coefficient for losses proportional to the speed squared (wind resistance) m is the mass of the vehicle g is gravity theta is the gradient of an incline that the vehicle is travelling up (negative if downhill) If the gradient is zero (flat road) you can forget the m.g.sin(theta) bit. The rest of the equation then becomes a simple second order polynomial. Working out k0, k1 and k2 is tricky. Usually this is done empirically by aquiring a long, straight piece of road and some accurate speed and time measurement equipment. You drive the car up to some speed (say 160 kph) and knock it out of gear. The vehicle will coast to a halt. The timing equipment logs the time the vehicle takes to coast down between pre-defined speed 'gates', say 10 kph each. You can apply some sort of curve fitting algorithm to the acquired data to get k0, k1 and k2. If your cheap you can use the linear regression tool in Excel or if you're a spod you can use the Downhill Simplex method, which is more suitable as the vehicle typically takes a long time to get to zero so the data has a very long tail. So now that you can work out both the losses at any speed and also the tractive force at any speed you're sorted because: Fa = Fe - Fl Where Fa is the actual accelerative force Fe is the tractive force supplied by the engin upon the road and Fl is the overall losses that we worked out above. Rearranging Newtons equation F=m.a to a = F/m where a = acceleration F = Fa m = vehicle mass So what you have to do now is run this calculation for very small increments of speed from 0 - 60 mph and work out the acceleration at each point. Fit a curve to the data and integrate it to get a curve for velocity against time. Then you can find out how long it takes to get to 60 mph. And when you've done all that remember that you have to allow a period of time for the gearchange and also somehow define another relationship for traction against velocity and you might get somewhere close. Good luck Edited to say: I forgot to mention clutch slip! You're on your own there mate

Edited by coopa, 16 August 2005 - 10:52 AM.

IIRC a standard NA makes around 120bhp peak at the wheels. I'd guess a standard VXT is around 160bhp. So you are probably not too far away, if using an average power figure and accounting for time lost during gear changes (probably around 0.5 sec per change?)

Do yourself a favour. Get in your car and see how quickly you can get to 60. The disparity between what you get and what you are calculating should tell you that the theory is not as simple as calculating an average power, all this comes down to is manipulating the numbers until you get the answer you want. It is not that simple. Sorry. I've dealt with students in their final year Automotive department at Loughborough university who are writing their thesis on this very topic. While the principles may be sound there are too many unknowns for this problem to be solved mathematically. They start out thinking they can do it but it is never long before the grim realisation that what they are undertaking is never going to be accurate hits them.

what coopa said in his first post .

As a small caveat here the modelling of tyre deformation and hysteresis is unbelievably complex

And on a slight side note, we tried to model hysteresis and stiction coeficients for various vehcules and tyres and conditions. and the conclusion was that it is a bit of a black art. the numbers sort of work, but there is often a lot of luck involved in these types of predictions. Basicly Mr Macadam or whatever his name was, was pretty lucky to find such a fantastic way of getting a machine to stay on a road.

Edited by JamesGray, 16 August 2005 - 12:31 PM.

It is not that simple. Sorry.

I don't think anyone was suggesting it was.

But if applying better input values to the simplistic formula above produces a result in the right ball park, then that's good enough for me. I still come out in a cold sweat when I hear a sentence starting with the phrase, 'Derive from first principles...'

I'll get me coat

It is not that simple. Sorry.

I don't think anyone was suggesting it was.

But if applying better input values to the simplistic formula above produces a result in the right ball park, then that's good enough for me. I still come out in a cold sweat when I hear a sentence starting with the phrase, 'Derive from first principles...'

If you need to know the answer before you tackle the question then what's the point?

Surely the idea of modelling something mathematically is that whatever you derive allows you to have some knowledge of what the car will do BEFORE it is tested. If by 'better input values' you mean finding figures that give you the answer that you already know then what have you learnt?

I made a calculation with Vehicle mass = 930 kg Front area = 1,5 m2 Cd = 0,38 Frictional losses = 15 % Average (engine) HP = 125 HP 0-100 kph (0-60) in 6,2 s

Ok here's my go using my theory above. I have used a vehicle model that roughly matches the vx and I use the average vehicle power used before. Transmission losses are taken care on in k0, k1, k2 k0 98.07 N k1 0 N/m/s k2 0.03204 N/(m/s)2 Mass 1000 kg Power 125 hp Power 88750 W Tyre Radius 0.25 m Tyre circumference 1.571 Clutch Slip factor: 0 mph = 0.25 1 mph = 0.5 2mph = 0.75 35 mph = 0.25 36 mph = 0.5 37 mph = 0.75 All other speeds it is 1 (ie no effect on performance) Add 0.5 sec for the gear change at an assumed 35 mph and I get 4.9 seconds. I'm surprised it came out so close but I don't like the shape of the curve at < 10 mph: Edit: The curve is this shape because we are using an average power, no bearing on reality!

Edited by coopa, 16 August 2005 - 02:37 PM.

Need to take into account gear changes, and the factors of gear ratio's, wheel/tyre slipage... Shall i go on... mathematical modeling is only as good as the data you put into the model. Put the wrong model together get the wrong answer. It's simple maths.... or not.

Edited by walkes, 16 August 2005 - 04:48 PM.

I made a calculation with

Vehicle mass = 930 kg
Front area = 1,5 m2
Cd = 0,38
Frictional losses = 15 %
Average (engine) HP = 125 HP

0-100 kph (0-60) in 6,2 s

If you add the 0,5 s for gear change in my calculation you get the 6,7 s which magazines have measured in tests.

I always try to calculate/foresee the expected result of my mods; why do anything if you don´t know what you are doing?

Need to take into account gear changes, and the factors of gear ratio's, wheel/tyre slipage... Shall i go on...

You are right of course. The plots worked out above however are based on an average engine power over the expected rpm range, thus negating the effect of gear ratio. I agree this is simplifying things too much.