GRAVITY-RACER ENERGY WORKSHEET
Use: Reproduce the fictional classroom examples with a calculator, then change one assumption. This is not a vehicle construction, ballast or operating guide. Organizer rules and inspections govern physical racing and testing.

ENERGY MODEL
Assumptions: start from rest near Earth's surface; g=9.81 m/s^2; use SI units; ideal case has no drag, rolling loss, braking or wheel rotational energy.
Mass m __ kg; vertical drop h __ m (not road length).
Available potential energy E=m*g*h = __ J
Ideal translation speed v=sqrt(2*g*h) = __ m/s
Convert m/s to km/h: multiply by 3.6.
Assumed energy assigned to losses and wheel rotation L __ J
Require 0 <= L <= E. Remaining translation energy K=E-L = __ J
Resulting v=sqrt(2*K/m) = __ m/s (m must be positive).
Fictional example: m=100 kg, h=30 m -> E=29,430 J; ideal v=24.26 m/s=87.3 km/h. L=6,000 J -> K=23,430 J; v=21.65 m/s=77.9 km/h. L is invented, not measured.
Constant rolling-force example: 10 N over 100 m consumes 1,000 J.

DRAG MODEL
Assumptions: still air, straight motion, density rho=1.20 kg/m^3, constant CdA=0.30 m^2. CdA is drag coefficient times its matching reference area.
D=0.5*rho*v^2*CdA in newtons; drag power P=D*v in watts.
v=5 m/s -> D=4.5 N; P=22.5 W
v=10 m/s -> D=18.0 N; P=180.0 W
v=15 m/s -> D=40.5 N; P=607.5 W
Change CdA to 0.15 at the same speeds: drag and drag power halve.
Doubling speed at fixed inputs quadruples drag and multiplies power by eight.
These steady-speed forces do not predict a course finish time. Changing wind, speed, rolling loss, wheel inertia and course geometry need a fuller model.

INTERPRETATION
What assumptions did you change?
Which quantities are measured and which are invented?
What evidence would be needed to compare actual cars?
Record repeated runs, timing method, course, start method, mass, wheels, alignment and weather, under approved event procedures.
Sources: https://pwg.gsfc.nasa.gov/stargaze/Senergy.htm
https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/drag-equation/
Historical manufacturer announcement: https://www.theautochannel.com/news/2005/08/19/140676.html
Example racing-program rules: https://www.soapboxderby.org/racers/commissions-committees-regional-directors/

YENRA ARTICLE: https://yenra.com/racing/gravity.html
Prepared September 7, 2026. Recheck the sources and applicability before use.