- #1

giulioooooh

- 5

- 1

- TL;DR Summary
- Basically, I'd like to create a function that displays speed or acceleration based on aerodynamic downforce which in turn is determined by speed. I'm not really getting any further with my math skills so I'm desperate for someone who actually knows what they're doing to tell me how easy this actually is.

First off: I'm currently working on an RC car heavily focused on aerodynamics for a Project I'd like to add to my Uni application. I've created a model, ran it through CFD and came up with some numbers. Now I'd love to plot out an equation that displays either speed or acceleration in dependence of time so I could tweak my Aero design. Turns out, I've got no clue of what I'm doing.

Here we go:

I'm trying to Calculate Downforce (aerodynamics and gravity) with this Formula:

F

And drag with this one:

F

(C being the coefficients of drag or downforce=lift, rho the air density, m being 50% of the total vehicle mass when accounting for 50:50 weight distribution)

These are the Formulas I found on the NASA website and I adjusted them to solve for Force.

Putting in my values I got out of CFD and some other rough calculations I came up with, I get these formulas:

F

F

(Yes, I know this is a lot of area, I just went with what CFD came up with since it doesn't really matter as long as both reference areas are the same)

or, simplified:

F

F

These equations seem to work fine and match up with CFD results for given speeds.

If I want to calculate the maximum possible acceleration, I've got to account for mass and tire grip. I decided to go for a traction coefficient

This gives me following equation that I'm kinda proud of, though I can't shake off the feeling that I've got something terribly wrong:

a

My current problem is that "(x)". The formula for acceleration is dependent on speed, which is very much self-referential and I've really got no idea on how to turn that into an equation that tells me speed or acceleration in relation to time.

Normally, you'd just have e.g. a(t)=s/t², the integral of that being velocity v(t)=a*t (I feel like this line is absolute bs but I'm too tired to really realize what exactly is wrong with it, though I think you get the idea.)

Furthermore, I've come up with the max acceleration the motors could output, calculated like this:

Torque=(9550*255W)/22500rpm=0.108Nm

F

a

So, can someone please help me out of my misery and give me some tips on how to create that function I crave which should tell me the acceleration in relation to time up until the point in time when max acceleration (limited by the motors) is achieved?

Thanks so much in advance guys and gals<3333

P.S: I'm in Europe and about to go to bed, so I'm sorry if I can't reply for the next like 10 hours, I'll try to get back to everyone bothering to put up with my (hopefully way too easy) questions

Here we go:

I'm trying to Calculate Downforce (aerodynamics and gravity) with this Formula:

F

_{downforce}=C_{downforce=lift}*rho*A*v²+g*mAnd drag with this one:

F

_{drag}=0.5*C_{drag}*rho*A*v²(C being the coefficients of drag or downforce=lift, rho the air density, m being 50% of the total vehicle mass when accounting for 50:50 weight distribution)

These are the Formulas I found on the NASA website and I adjusted them to solve for Force.

Putting in my values I got out of CFD and some other rough calculations I came up with, I get these formulas:

F

_{downforce}(x)=0.073*(1.225kg/m³)*6245cm²*(x*m/s)²+(9.81N/kg)*400gF

_{drag}(x)=0.5*0.052*(1.225kg/m³)*6245cm²*(x*m/s)²(Yes, I know this is a lot of area, I just went with what CFD came up with since it doesn't really matter as long as both reference areas are the same)

or, simplified:

F

_{downforce}(x)=0.056N*x²+3.924NF

_{drag}(x)=0.02N*x²These equations seem to work fine and match up with CFD results for given speeds.

If I want to calculate the maximum possible acceleration, I've got to account for mass and tire grip. I decided to go for a traction coefficient

*μ*0.9 and a total mass m_{t}=_{total}=800g. (Quick question: the traction coefficient also accounts for tire contact patch right?)This gives me following equation that I'm kinda proud of, though I can't shake off the feeling that I've got something terribly wrong:

a

_{max}(x)=(F_{downforce}(x)*0.9-F_{drag}(x))/800gMy current problem is that "(x)". The formula for acceleration is dependent on speed, which is very much self-referential and I've really got no idea on how to turn that into an equation that tells me speed or acceleration in relation to time.

Normally, you'd just have e.g. a(t)=s/t², the integral of that being velocity v(t)=a*t (I feel like this line is absolute bs but I'm too tired to really realize what exactly is wrong with it, though I think you get the idea.)

Furthermore, I've come up with the max acceleration the motors could output, calculated like this:

Torque=(9550*255W)/22500rpm=0.108Nm

F

_{1motor}=0.108Nm/2.5cm*sin(90)=4.32N => F_{2motors}=2*F_{1motor}=8.64Na

_{max}=8.64N/800g=10.8m/s² (not accounting for drag and with infinitely high downforce that doesn't crush the car)So, can someone please help me out of my misery and give me some tips on how to create that function I crave which should tell me the acceleration in relation to time up until the point in time when max acceleration (limited by the motors) is achieved?

Thanks so much in advance guys and gals<3333

P.S: I'm in Europe and about to go to bed, so I'm sorry if I can't reply for the next like 10 hours, I'll try to get back to everyone bothering to put up with my (hopefully way too easy) questions