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Name: James B.
Status: other
Age: 20s
Location: N/A
Country: N/A
Date: 2000-2001

I am developing a software package to analyse vehicle performance. I have lateral and longitudenal g-force data for a vehicle as it moves. I wish to plot the path of the vehicle given the data. My physics is a little rusty! Can anyone help? The data I have is as follows:

time (s), Lateral G (G), Longitudenal G (G). The longitudenal G is either positive indicating acceleration or negative indicating deceleration. The lateral G data, however is negative for a left turn and positive for a right turn.

What are the equations I need?

What you have is the acceleration of the vehicle in units of 9.8m/s^2 or 32ft/s^2, depending on whether you want to use metric or English units. Convert from g-factor to appropriate units. If you want to plot position vs time, you will need two more pieces of imformation: initial position and initial velocity. Since you are dealing with a three-dimensional system, each of these requires 3 coordinates: initial (x,y,z) and initial (Vx,Vy,Vz). There are several ways to add the effects of acceleration onto current position and velocity. One of the easiest is to assume that acceleration is constant over each individual time duration. Assume at t=0 the current velocity components and position components are the initial values: t=0, x=x0, y=y0, z=z0, vx=vx0, vy=vy0, vz=vz0.

Let dt=new time minus current time, then change current time to new time. Adding the z-axis is easy. You have the acceleration in the z-direction isolated:

new z = z + (vz)dt + (1/2)(az)(dt)^2

new vz = vz + (az)(dt)

(Order is important: do not change vz until new z has been calculated)

As for x and y coordinates, the lateral acceleration must first be separated into coordinates. This depends on the horizontal direction. The horizontal vector indicating direction of motion is (vx/v , vy/v), where v=sqrt(vx^2 + vy^2). Note: If v=0, you will have to use the previous direction vector. The "lateral" vector, perpendicular and to the right(positive) is (vy/x , -vx/v). Multiply this by the lateral acceleration to get the acceleration coordinates:

ax=(lat.acc.)(vy/v) , ay=(lat.acc)(-vx/v)
(acceleration in proper units).

Calculate new position and velocity in both x and y directions as done for z.

Dr. Ken Mellendorf
Illinois Central College

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