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Can someone confirm that I am doing this correctly? Fairly certain that I am, just want to make sure.
The car is a FSAE RWD with a T2 Diff. Looking at page 39 of "Fundamentals of Vehicle Dynamics" by Thomas D. Gillespie, it states that for a solid rear axle with a locking differential the maximum tractive force is
Fx=u*(W*b/L)/(1-(h/L)*u)
and thus the maximum longitudinal acceleration is
axMAX=Fx/(Vehicle Weight/g)
Correct??
Can someone confirm that I am doing this correctly? Fairly certain that I am, just want to make sure.
The car is a FSAE RWD with a T2 Diff. Looking at page 39 of "Fundamentals of Vehicle Dynamics" by Thomas D. Gillespie, it states that for a solid rear axle with a locking differential the maximum tractive force is
Fx=u*(W*b/L)/(1-(h/L)*u)
and thus the maximum longitudinal acceleration is
axMAX=Fx/(Vehicle Weight/g)
Correct??
Hey,
I don't know about the first equation because I can't find what all symbols mean.
The second one is definitely inaccurate. Weight/g is just fancy-shmancy for "mass", but not exactly the same for a car. According to a = Fx/(W/g), if you have aerodynamic lift, you would suddenly have less mass to accelerate.
But more importantly there is no drag/rolling resistance (front wheels..) in your model.
Maybe you can list the symbols of that first equation.
Best,
Erik
Gillespie uses some very basic assumptions in his analyses. This is because his book is "Fundamentals" not "Advanced".
I think one of the assumptions in the tractive force example will be tyre mu = 1. For the maximum acceleration, aero drag may have been neglected as Erik points out.
Aero lift is probably also neglected.
The assumptions are clearly stated, so you should be able to work out for yourself whether they are valid for your case.
Regards, Ian
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by murpia:
Gillespie uses some very basic assumptions in his analyses. This is because his book is "Fundamentals" not "Advanced".
I think one of the assumptions in the tractive force example will be tyre mu = 1. For the maximum acceleration, aero drag may have been neglected as Erik points out.
Aero lift is probably also neglected.
The assumptions are clearly stated, so you should be able to work out for yourself whether they are valid for your case.
Regards, Ian </div></BLOCKQUOTE>
Actually the assumptions are not clearly stated in the book. The only thing I can find is u=peak coefficient of friction and instead of using that, I am using instantaneous coefficient of friction based on my tire model.
b=longitudinal distance from the front axle to center of gravity
u=peak coefficient of friction
W=weight of the vehicle
L=wheelbase
Fx=force in the x-direction(tractive force)
There is no assumption about mu=1, that doesn't even make sense because why put it into the tractive force equation if its equal to 1?
Fx = mu * dynamic rear weight (for a rwd car)
dynamic rear weight = W * a / (a+b-h*mu)
a = distance from front axle to cg
b = distance from rear axle to cg
h = cg height
mu = coefficient of friction
W = total weight
Adding Downforce can increase your dynamic rear weight and increase your Fx. However, it doesn't change your mass, so your acceleration will still be force/mass.
----
Mike Cook
It's an engineering competition, not an over-engineering competition!
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Mike Cook:
Fx = mu * dynamic rear weight (for a rwd car)
dynamic rear weight = W * a / (a+b-h*mu)
a = distance from front axle to cg
b = distance from rear axle to cg
h = cg height
mu = coefficient of friction
W = total weight
Adding Downforce can increase your dynamic rear weight and increase your Fx. However, it doesn't change your mass, so your acceleration will still be force/mass. </div></BLOCKQUOTE>
Thanks man, what I was looking for.
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Mike Cook:
Fx = mu * dynamic rear weight (for a rwd car)
dynamic rear weight = W * a / (a+b-h*mu)
a = distance from front axle to cg
b = distance from rear axle to cg
h = cg height
mu = coefficient of friction
W = total weight
Adding Downforce can increase your dynamic rear weight and increase your Fx. However, it doesn't change your mass, so your acceleration will still be force/mass. </div></BLOCKQUOTE>
mu in this case is the peak coefficient of friction or the coefficient of friction at the dynamic weight?
Well, technically, it would be the coefficient of friction for the tire with the dynamic weight on it. But you would probably need a good deal of tire data to figure that out (and it would still be wrong).
With our tires, I usually use about 1.4 as a good starting point.
----
Mike Cook
It's an engineering competition, not an over-engineering competition!
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Mike Cook:
Well, technically, it would be the coefficient of friction for the tire with the dynamic weight on it. But you would probably need a good deal of tire data to figure that out (and it would still be wrong).
With our tires, I usually use about 1.4 as a good starting point. </div></BLOCKQUOTE>
Why would it still be wrong? I am using tire data from the tire consortium
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