TeeLew
Well-Known Member
OK, so let's have a discussion about our assumptions concerning the experiment and the potential areas measurement error. Our friend GTX was touching on this, even if in a disingenuous manner.
Assumptions (which perhaps Steeda would chime in on?):
Wheel set A & B are the same size.
Wheel set A & B distribute their mass in a similar manner, so the difference in moment of inertia is the same as the difference in the mass.
The difference in Tire set A & B are minimal in terms of size, pressure and rolling resistance qualities.
The difference in the car tie down is minimal.
The difference in ambient conditions is minimal and corrected for accurately by the dyno software.
The overall gearing is the same for A & B.
The car wheels and dyno drum is going through the same rotational speed range in the same amount of time (this is a big and difficult to account for area for error).
The engine itself is making the same HP in both runs and the losses through the drivetrain remain stable.
There are likely a bunch of other assumptions that we need to make to accurately account for the variables which we're dealing, but this gives us an idea of what we're trying to accomplish and the errors which might be introduced.
Rotational kinetic energy is a well understood phenomena. We use flywheels for all sorts of energy storage, so we aren't exactly breaking new ground here. The most important thing to understand is that this energy varies with the square of rotational speed, not linearly. The difference between 110 & 120 mph is much greater in terms of rotational kinetic energy than that of 10 and 20 mph, even though the speed difference between the two is the same. Had I been running the test, I probably would have ran each test 3-5 times producing a nominal baseline with which to compare our experimental data to increase the confidence in our numbers.
The Steeda dyno sheet shows it's biggest differences at the top of it's speed range while at the bottom of the range, the curves are essentially perfect overlays. This is exactly what we would expect. When the wheels are spinning at a rate where they have a limited ability to sink power, they don't affect our dyno graph. When they are spinning at their maximum speed, thus in the range where they have the greatest ability to sink power, we see the biggest differences in the graphs.
The gearing issue is important to cover. This could be a different gear in the transmission, final drive or just a different tire height. The dyno sheet has engine power w.r.t. engine RPM, but we are actually measuring the power w.r.t. wheel (or drum if you prefer) rotational speed and then marrying those numbers with engine RPM in our dyno software. If our gearing changes, it will not effect the power that the engine produces, but it will effect what we measure because our frictional losses, like the transmission, final drive or tire rolling resistance will be different. It will also effect things like the rotational speed of the wheels, which is to say the energy they'll sink during the test.
We can calculate an estimate of the power it takes to accelerate a wheel/tire from rotational speed A to B by estimating the rotational inertia. We don't have real moment of inertia data, but we can estimate. So while I was watching Netflix with my son last night, I ran the numbers comparing two wheels. I modeled a 30# wheel versus a 20# wheel, both with a 30# tire. I started with a disc surrounded by a thin-wall hoop and then modeled the tire as a 30# thick hoop. I started by accelerating the 'car' from 0-120mph. I used a tire with a rolling circumference that gives 750 rotations per mile, which gives an angular speed of 157.1 rad/sec at 120 mph.
I assumed acceleration was constant from 0-120 mph and the car did it in 10 seconds, so a constant 12 mph/sec acceleration. I'm looking at purely rotational acceleration; there's no component of linear acceleration of the mass itself (like on the dyno or a wheel balancer). As the speed increases, it takes more and more power to maintain this rate of acceleration.
So what's do the numbers say? At 120 mph, it takes 4.7 HP to maintain the constant acceleration for the 60# wheel/tire. For the 50# wheel/tire, it takes about 4.2 HP. So the power difference to maintain this acceleration rate is about 1/2 HP at 120 mph. All four wheels together, regardless of whether or not they're hooked to the driven axle, will store the same amount of energy and so the total shift is about 2 HP at high speed.
The 6 HP discrepancy (about 6x what I've calculated) which Steeda has measured on their dyno is probably a product of a couple different things. The first is that it's probably accelerating at a greater rate than 12 mph/sec. The second is that it might be at a higher speed than 120 mph (although, even the factor limit speed of 155 mph doesn't change the difference appreciably). Our biggest difference in the measurement is the dyno itself, which is perhaps going to have a 1-2% measurement error. What I've determined is something like wheels, which undoubtedly has an effect on the acceleration of the car, is probably too small of a difference to effectively measure on a roller dyno.
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