Run-time estimator
Real race-car engineering, sized for you. The same physics engine runs at every level — Easy gives you big choices and plain words, Intermediate opens up the numbers and shows where the energy goes, Advanced hands you every coefficient, the equations, and the tools to measure them on your own car.
What's going on?
Gravity is your engine. At the top of the hill your car is holding — of energy (that's about — — the work of lifting a — lb car up — ft). Rolling down turns that stored energy into speed.
Four things steal it on the way down: squishy tires rubbing the road, air that has to get out of the way, bearings that fight the axle, and heavy wheels that have to be spun up. Right now your biggest energy thief is —, eating — of what gravity gave you.
Top tips for your car
Try it: change one thing at a time and watch the time. That's exactly how real engineers test — one change, measure, repeat.
The forces on your car
Only the part of gravity pointing down the slope pushes you: F = m·g·sin(θ). On your —% grade that's — N for a — lb car. Steeper hill or heavier car = more push.
Tires flatten a little where they touch the road, and squishing rubber wastes energy. F = Crr × weight. Your total Crr is —, about — N of drag the whole way down. Hard tires, high pressure and straight wheels keep it small.
Friction in the bearing makes a tiny twisting force (torque). Divided by the wheel radius it becomes a drag at the road — so bigger wheels shrink bearing drag. Yours adds about — N. Clean and lightly oiled beats thick grease.
F = ½·ρ·Cd·A·v². It grows with the square of speed: twice as fast = four times the push. At your top speed (— mph) the air pushes back with — N. Your frontal area is — ft² — sit low, build narrow.
Wheels don't just move forward, they spin, and spinning takes energy too. A wheel acts like it weighs k × its mass extra (k = — for yours). Your car "feels" like — lb when accelerating. Light rims, heavy hubs.
Gravity's push grows with mass, rolling resistance grows with mass (they cancel), but air drag does not care about mass. So a heavier car shrugs off the air better — until the division weight limit. Put ballast low and between the axles.
Measure it on your real car
- Slope: put a 4-ft level on the road, lift one end until the bubble centers, measure the gap. Gap ÷ 48 in × 100 = % grade. Do it in three spots and average.
- Rolling + bearing drag (coast-down): on flat pavement, push the car to a walking speed (about 3 mph), let go, measure how far it coasts. Crr ≈ v² ÷ (2·g·d). Example: 1.34 m/s and 11 m → 0.0083.
- Bearings alone (spin test): lift a wheel, spin it with the same flick each time, time how long it turns. Longer = less drag. Compare before and after cleaning.
- Frontal area: have the driver sit in the car, measure the widest and tallest points. Area ≈ width × height × 0.85.
The model, exactly
m = m_driver + m_car + n·m_w m_eff = m + n·k·m_w (rotational KE = ½·I·ω² with I = k·m_w·r², ω = v/r ⇒ ½·k·m_w·v²)
F_g = m·g·sinθ F_r = Crr·m·g·cosθ, Crr = Crr_tire·(12/d_in)^0.35 + Crr_surface + 0.7·sin(toe)·(n_misaligned/n)
F_b = μ_b·m·g·cosθ·(r_bore/r_w) + n·τ_drag/r_w (load-proportional contact friction, plus seal/grease torque leveraged by the wheel radius)
F_d = ½·ρ·Cd·A·(v+w)·|v+w|, ρ = p/(R·T) with p from the standard atmosphere at your altitude
a = (F_g − F_r − F_b − F_d) / m_eff, integrated with a fixed step dt over the ramp (θ = asin(h/L)) then the run (θ = atan(grade)). Static check: if F_g ≤ F_r + F_b at v = 0, the car never starts.
Energy check: ∫F_g ds = ½mv² + ½n·k·m_w·v² + ∫F_r ds + ∫F_b ds + ∫F_d ds. The budget table is those integrals; if it doesn't sum to 100% the time step is too coarse.
Safety: brake must absorb ½·m_eff·v² (shown right); stopping distance d = v²/(2·μ·g) with μ = 0.6 for a drag brake on dry asphalt; tip-over when lateral acceleration exceeds g·(track/2)/h_cg, i.e. a turn tighter than v²/a_lat at speed.
Assumptions & limits (engineers always list these)
- Rigid car, no suspension losses; constant Crr (real tires: Crr rises slightly with speed and drops with pressure).
- Bearing μ and τ are constants; real seal drag depends on temperature and speed. Measure, don't trust the preset.
- Cd is a guess unless you test it: coast-down at two speeds separates the v² (aero) term from the constant (rolling) term.
- Toe scrub uses a flat lateral μ of 0.7 — a simplification of tire slip-angle behaviour.
- No steering losses, no wind gusts, no track crown. Treat results as ±5–10%, and use A/B comparisons (same assumptions on both cars) rather than absolute times.
Measurement procedures
- Two-speed coast-down (separates rolling from aero): on flat ground coast from v₁ and v₂; deceleration a = Crr·g + (ρ·Cd·A/2m)·v². Two equations, two unknowns.
- Tilt test for static resistance: raise one end of a long board until the car just keeps rolling at steady speed; Crr_total = tan(θ) — that is the number the static-start check uses.
- Wheel inertia (k): race the wheel against a solid disc (a hockey puck works — mass doesn't matter) down the same short incline and time both; k = 1.5·(t_wheel² / t_disc²) − 1, because a rolling object accelerates at g·sinθ/(1+k).
- CG height: weigh the front axle on level ground, then with the rear raised a known height; the shift in front-axle weight gives h_cg = (ΔW·L)/(W·tanφ) + r_w.
- Air density: read temperature and pressure from a phone weather app on race morning; a 20 °F swing moves ρ about 4%.
Where did the energy go?
| Where it went | Joules | ft·lb | Share |
|---|
Safety numbers
- Speed leaving the ramp
- —
- Energy the brake must absorb
- —
- Stopping distance (drag brake, dry)
- —
- Lateral g before tipping
- —
- Tightest turn at top speed
- —
The run-out area past the finish must be longer than the stopping distance. A high seat or narrow track lowers the tipping limit — that's why the rules cap height and require a stable seat.
What would make it faster?
Each row changes one thing and re-runs the simulation. Change one variable at a time — that's the engineering method.