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I just saw your post from last week re: integrating engine performance curves.
You have to be careful what you're integrating, and the units involved. Horsepower (energy / time) and Torque (energy) are typically plotted versus rpm, which has units of (1 / time), as opposed to time. So, if you integrate a torque curve over the engine's rpm range, your result is (energy / time), or power. Integrating the torque curve thus gives you the total power output of an engine as it runs through it's rpm range. If you were to integrate the power curve, you get (energy / time^2), or the rate of change of power delivery. This is something quite different.
In talking about the potential for motive force (thus acceleration), what is of interest is the power delivery of the engine through the rpm range. As noted, this quantity is determined via integration of the torque curve. A power curve is useful for determining the instantaneous power available at a given rpm (which given a gear and vehicle geometry, translates to a given speed). This instantaneous available power determines whether a vehicle has sufficient capability to "move through" a certain speed range. This is useful, for example, in calculating the theoretical top speed.
Your relationship of total work to change in kinetic energy is applicable, except that you need to consider that not 100% of the work produced by an engine is capable of being applied toward acceleration of the vehicle. You have to get the energy from the motor to the ground. That requires at least two major interfaces, namely motor/transmission and tires/ground. The first always has a significant amount of loss. The second has limits on how much energy can be transmitted. Also, not all of the energy produced by the motor goes toward linear acceleration of the vehicle. You also have changes in kinetic energy of all the spinning parts in the transmission., as well as frictional losses to aerodynamic drag and rolling resistance.
The biggest problem though is that you don't know just from looking at a torque or power curve how much total energy the engine puts out. To know that you'd have to know how much time it took to move through the rev range. And to know that you have to know all the details of the transmission, vehicle geometry, friction forces, inertial losses, etc. etc. etc. that I've been talking about above. In short, you have to use the performance curve as one input of a theoretical acceleration performance model. It won't explicitly tell you that information by itself.
You could calculate how much work (energy) it takes to get a vehicle from one speed to another, taking into account all the energy storing & dissipating elements. Then, integrating the torque curve over the appropriate rev range, you could find the maximum power output of the engine through that speed range. The time it takes to deliver that energy could then be found, provided you made some assumptions about the effective efficiency of the vehicle in delivering the energy (would depend on gearing, geometry, transmission losses, etc.). This problem isn't any simpler though.
I have a finite difference model (excel spreadsheet) which calculates instantaneous acceleration at small time steps in order to estimate acceleration performance. It considers the performance curve, gearing, vehicle geometry and parameters (Cd, weight, etc.), aerodynamic drag, transmission losses (estimated), acceleration dynamics (i.e. weight shifting from front to rear), tire traction, and shift times. However, it's lacking in that it does not (currently) model rolling resistance, inertial effects, or the differences between dynamic and static engine response. Dean over on the performance board pointed the last one out to me; namely the fact that your engine doesn't perform the same way when accelerating dynamically as it does when given time to reach a steady state condition at each rpm spot on the published torque curve, due to lovely things like turbo lag, amongst other things.
Thus, my particular model is limited in the accuracy with which it can compare cars. However, it does a decent job, and I've been able to correlate it pretty well with published test results. For similar cars, I can do a pretty fair comparison. That's why I'm anxious to get my hands on tech data for the new 9-3SS. Theoretically, unless there are big differences in abilities to handle turbo lag or put power on the road, my model should be able to predict with a faid degree of accuracy the relative performance between an "old" 9-3 and the new one.
Anyway, hope this clarifies things. Maybe you could make a better model!
'Roo
posted by 12.13.238...
, Thu, 10 Oct 2002 14:51:21
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