Pinewood Derby Speed Calculator: Finish Time, Speed and What Each Tweak Is Worth
Predict a pinewood derby car’s finish time, speed at the bottom of the ramp, finish speed and scale speed from the track’s drop and length, the car’s weight and centre of gravity, wheel mass, wheels touching and axle prep. See how many milliseconds each change buys (moving the CoG back, reaching the 5 oz limit, better axles, lighter wheels, raising a wheel), a speed-along-the-track chart and an energy budget of where the potential energy goes.
How it works
θ = asin(drop ÷ ramp length) · effective drop = drop + (CoG distance behind the nose) × sin θ · potential energy = m g h · while the CoG is on the slope: drive = m g sin θ · losses: friction = c × normal force with c = µ × r_axle ÷ r_wheel + 0.008 (tread) + 0.001–0.003 (rail), drag = ½ ρ C_d A v², wheel spin adds ≈ 0.7 × wheel mass per turning wheel · a = (drive − friction − drag) ÷ (m + spin mass), integrated until the nose crosses the finish · scale speed = average speed × scale
A pinewood derby car is a gravity machine: everything it does is paid for by the height its centre of gravity falls, and the race is decided by how little of that energy is wasted before the nose crosses the line. Mass helps because the energy grows with it while friction against the guide rail and air drag largely do not. A rearward centre of gravity helps because the CoG starts higher up the slope and keeps pushing the car for longer: in this model the car is driven by gravity until its CoG, not its nose, reaches the bottom. Light wheels help because spinning them up costs energy, and polished, lubricated axles and a raised front wheel cut friction directly. The calculator integrates those forces down the ramp and along the flat in half-millisecond steps, so it can put a number in milliseconds on each tweak: moving the CoG back, reaching the 5 oz limit, better axle prep, raising a wheel and lighter wheels. It also gives the speed at the bottom of the ramp and at the finish, the scale speed, the time one car length is worth at the line, an energy budget and a chart of speed along the track. Friction, drag and the wheel inertia are typical values for a standard 7 in car on BSA wheels, and the curved transition and track joints are not modelled, so use the times to compare builds rather than as exact lane times.
Worked example
On a 32 ft track with a 48 in drop over a 96 in ramp (30°), a 5 oz car with its CoG ¾ in ahead of the rear axle, stock 2.6 g wheels, four touching and polished graphited axles has its CoG 5.25 in behind the nose, so it starts 2.6 in higher (effective drop 50.6 in) with about 1.79 J of energy. The model gives a run of about 2.63 s, 10.7 mph (4.80 m/s) at the bottom of the ramp and 9.9 mph at the finish, with about 77% of the energy reaching the line as forward motion, 4% as wheel spin, 12% lost to friction and 7% to air drag. Lighter 1.5 g wheels (about 26 ms) and raising a front wheel (about 25 ms) are the biggest levers, pro-level axle prep saves about 14 ms and moving the CoG back another half inch about 4 ms. One car length at the finish is about 40 ms, and the average speed of 8.3 mph is about 208 mph at 1:25 scale.
Sources: Wikipedia: Pinewood derby (rules, 5 oz weight limit, track and car basics)
Frequently asked questions
Why does weight matter if all objects fall at the same rate?
In a vacuum they would tie. On a real track, air drag and the rubbing on the centre rail do not grow with the car’s mass, so a heavier car has proportionally more energy to spend against the same losses. That is why fast cars are right at the 5.0 oz limit.
Is a far-back CoG always better?
It is faster in theory but less stable: a car balanced near the rear axle can wobble, rub the rail or lift its front at the transition unless the axles are straight and aligned. For a first build, 1–1.25 in ahead of the rear axle is a safe, fast compromise.
How much faster is a car on three wheels?
In this model, raising one front wheel removes one wheel to spin up and some rubbing, worth roughly 15–25 ms on a typical track: about half a car length. Check that your pack allows it.
How fast does a pinewood derby car go?
On a track with a 4 ft drop the fastest cars reach about 10 mph (4.5 m/s) at the bottom of the ramp and finish a 32–42 ft track in 2.4–3.0 s. Scaled up to a real car (1:25) that is an average of around 200–250 mph.
What matters most for a fast car?
Reaching the weight limit, smooth polished axles with graphite, straight alignment and a rearward CoG. Small differences add up: race margins are often 10–50 ms, less than two car lengths.
Related calculators
A simplified physics model; real tracks have curved transitions, joints and imperfect alignment, and wheel and axle behaviour varies. Follow your pack's rules on weight, dimensions, lubricants and wheel modifications.