Equations of Motion Under Constant Power

[Eddie W. Shore]

The following HP Prime program, CARFORCE, takes the following for arguments:

P = power in horsepower (hp)
M = mass in pounds (lb)
I = initial velocity (mph)
T = time to evaluate (seconds)

CARFORCE will return a list of four answers:

Zip (numerical value only (ft/s^1.5))
Acceleration in miles per hour per second
Velocity in miles per hour
Position in feet

Example:

Data: Vehicle has a 100 hp engine, has a mass of 4,000 pounds. Figure the equations of motion after 10 seconds elapsed. Assume the vehicle is initially stopped.

CARPOWER(100, 4000, 0, 10) returns

{21.0331445022, 3.2066959696_mile/(h*s), 64.1339193918_mile/h, 627.087211833_ft}

Program:

Code:

EXPORT CARPOWER(P,M,I,T)
BEGIN
// 2014-06-14 EWS
// Roger Stevenson, 1980
// Lloyd W. Taylor, 1930
// power (hp),mass (lb), 
// initial velocity (mph), time (sec) 
LOCAL Z,W,A,V,X,L0;
// convert
P:=CONVERT(P*1_hp,1_(ft*lbf/s))/1_(ft*lbf/s);
I:=CONVERT(I*1_mph,1_(ft/s))/(1_(ft/s)); 
M:=CONVERT(M*1_lb,1_(slug))/(1_slug);
Z:=√(P/M);
// temp
W:=2*T+I²/Z²;
A:=Z/√W;
V:=Z*√W;
X:=Z/3*(W^1.5-(I/Z)^3);
L0:={Z,A*15/22,V*15/22,X};
L0:=L0*{1,1_(mile/(h*s)),1_(mile/h),1_ft};

RETURN L0;

END;

Sources:

Lloyd, Taylor W. “The Laws of Motion Under Constant Power” The Ohio Journal of Science, v30 n4 (July, 1930), 218-220. https://kb.osu.edu/dspace/bitstream/1811...04_218.pdf

Revised 6/12/2014

Stephenson, Roger “Constant power equations of motion” (Published January 29, 1982) from the compilation book The Physics of Sports edited by Angelo Armenti, Jr. American Institute of Physics: New York 1992, pp. 284-289

My blog entry: http://edspi31415.blogspot.com/2014/06/h...under.html