Mechanical Engineering

# Modelling vehicle acceleration

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Hi everybody

I am an undergraduate mechanical engineering student and I am currently working on a project.

I need to model the acceleration of a motorcycle from 0-100mph, taking into account road friction and drag friction, the gear ratios, power/torque curve etc.

I am completely at a loss on how to do this, so I would appreciate any help I could get with this. It will be a simple flat surface so I just need a "time taken" from 0-100mph.

I have the frontal area, wheel radius, power/torque curves against RPM, gear ratios etc. Also the vehicle mass and an estimated drag coefficient.

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This is a typical example of solving an ordinary nonlinear differential equation. The details can be found in Chapter 1 of my book, Living Math, which you can read (click on "Look Inside") without buying the book. The eBook will be free on March 9th. The method to use is 4th Order Runge-Kutta, explained in Appendix B. The software is free at the link listed in the Forward. Further details can be found in my book, Differential Equations, which will be free on March 4th. The car simulation in Chapter 3 includes rpm, torque, and gear ratios. The calculations are included in the free source code package (car_simulation.c) and a spreadsheet (car_simulation.xls), also free online. There's another example calculating projectile drag. I have attached several files. https://www.amazon.com/author/djamesbenton

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On 3/2/2021 at 9:20 PM, dudleybenton said:

This is a typical example of solving an ordinary nonlinear differential equation. The details can be found in Chapter 1 of my book, Living Math, which you can read (click on "Look Inside") without buying the book. The eBook will be free on March 9th. The method to use is 4th Order Runge-Kutta, explained in Appendix B. The software is free at the link listed in the Forward. Further details can be found in my book, Differential Equations, which will be free on March 4th. The car simulation in Chapter 3 includes rpm, torque, and gear ratios. The calculations are included in the free source code package (car_simulation.c) and a spreadsheet (car_simulation.xls), also free online. There's another example calculating projectile drag. I have attached several files. https://www.amazon.com/author/djamesbenton

Thank you so much. I will have a look at this

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On 3/2/2021 at 9:20 PM, dudleybenton said:

This is a typical example of solving an ordinary nonlinear differential equation. The details can be found in Chapter 1 of my book, Living Math, which you can read (click on "Look Inside") without buying the book. The eBook will be free on March 9th. The method to use is 4th Order Runge-Kutta, explained in Appendix B. The software is free at the link listed in the Forward. Further details can be found in my book, Differential Equations, which will be free on March 4th. The car simulation in Chapter 3 includes rpm, torque, and gear ratios. The calculations are included in the free source code package (car_simulation.c) and a spreadsheet (car_simulation.xls), also free online. There's another example calculating projectile drag. I have attached several files. https://www.amazon.com/author/djamesbenton

Hi @dudleybentonI have read that chapter thank you. The bit I am really struggling with is integrating the air resistance and road load resistance into this - could you advise?

Thanks

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Resistance (air, road, rolling, drag, whatever) are all forces in the direction opposite of forward motion (i.e., -F). What you're integrating is Newton's 2nd Law or ΣF=d(mV)/dt where F and V are both vectors. In this case there's only one direction so the vector notation isn't necessary  and dm/dt is negligible. RK4 (or Euler's method in an Excel spreadsheet) integrates A=ΣF/m=dV/dt and then V=dX/dt. The engine is providing +Power/V less the Drag so that dV/dt=P/V-D. P is a function of rpm, which is a function of V and gear ratio. D is a function of V.

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