Speed Science
Thermal dynamics
Rank the thermal effects on a gravity car by size. Air density is the largest and you do not control it, wheel and axle temperature is the one you might, surface colour is a distant third, and rising hot air is not an effect at all.
ILLUSTRATED THERMAL BUDGET
Put the thermal effects on one axis before choosing one to chase.
buoyancy check: Ri = g·β·ΔT·L / v²
- ρ
- air density in kg/m³
- p, T
- absolute pressure in Pa and absolute temperature in K
- R
- specific gas constant for air, about 287 J/(kg·K)
- β
- thermal expansion coefficient, about 1/T for a gas
- Ri
- Richardson number: buoyancy divided by inertia. Below about 0.1 buoyancy is not participating.
Illustrative density example, not a target
An 18 °C morning and a 30 °C afternoon are 291.2 K and 303.2 K, a density ratio of 0.960 and so a 4.0% thinner air. On the reference run that removes about 81 J from a 2,030 J drag bill without anyone touching the car. The same run gives Ri near 0.008 for a 20 K warm shell, which is why the bottom bar of the chart is empty.
Bar lengths are relative sizes on the illustrative run declared below, not measurements from your car. The wheel and axle bar is drawn at the same order as air density because the mechanism is that strong; its actual size on your wheels is a measurement you still owe yourself.
GARAGE WORKSHEET
The minimum record needed to act on this guide.
QUESTION THIS STATION ANSWERS
Did a thermal change move the clock by more than the weather moved the air on the same day?
BRING
- Infrared thermometer for shell, axle trees, each wheel hub, and the track surface
- Temperature, barometric pressure, humidity, and wind speed with direction
- Timing system, wheel and lane map, and a randomized paired A/B run sheet
LOCK BEFORE READING
- Legal finish, coating, wheel, and axle state confirmed against the current plan before any run
- Driver, posture, ballast, wheel IDs and positions, lane, and release method
- Staging sun exposure and time-in-sun held equal across both halves of every pair
WRITE THE RAW RECORD
- Air temperature, pressure, humidity, and wind on every run, not once per session
- Shell, axle tree, hub, and track temperatures taken at a marked spot and a marked time before each run
- Randomized paired run order, order reversal, and the within-condition spread
DECISION GATE
Report the result as unresolved when it is smaller than ordinary run-to-run spread, when the pair straddled a weather change, or when it disappears after order reversal. Reject any finish, coating, or wheel conditioning the current plan and inspector do not permit, whatever the timing sheet says.
VERIFY NEXT
Replicate on another day and lane, then test the wheel and axle temperature mechanism on its own before crediting anything to the shell.
RANK THE EFFECTS BEFORE YOU CHASE ONE
Heat does change a run. It does not change it where the pits usually look.
Every thermal argument in gravity racing eventually turns into an argument about paint. That is the smallest of the four effects on this page, and the largest one is not on the car at all. Before spending a season on finish, put the effects on one axis and look at the sizes.
| Effect | Mechanism | Size on the reference run below | Do you control it? |
|---|---|---|---|
| Air density | Warm, low-pressure, humid air is thinner, so every drag force falls with it | About 4% of the drag bill between a cool morning and a warm afternoon, near 80 J out of a 3,360 J loss budget | No. Log it, or it corrupts every test you run. |
| Wheel and axle temperature | Lubricant viscosity and wheel material hysteresis both fall as temperature rises | Mechanism is real and the same order as density. The size is specific to your wheels and must be measured. | Partly, and only if your rule book allows it. Ask first. |
| Surface temperature and finish | Wall heat transfer shifts skin friction and boundary-layer transition | Small, and the sign is not the one Derby Tech published. Its own author measured about six inches. | Yes, within the plan, and it is governed. |
| Hot air rising off the shell | Buoyancy lifting warm air out of the oncoming flow | None. About 8 mm of drift inside a 42 mm boundary layer. See the myth table. | Not applicable. |
Nothing on this page outranks a binding wheel, a crossbound frame, or a driver who corrects three times on the ramp. Thermal work is the last quarter inch of a setup. Stations one through eight of the Setup Lab come first.
THE REFERENCE RUN
Every number above is auditable against this one illustrative car.
Effect sizes mean nothing without the run they are measured against, so this page declares one and uses it throughout. Every figure here is an illustrative generic example, not a setup target, a rule limit, or a prediction for your hill.
combined car and driver 91 kg, so W = 893 N
finish speed 13.1 m/s (29 mph), body length 2.0 m
A = 0.25 m², Cᴅ = 0.45, ρ = 1.20 kg/m³
That closes an energy budget you can check:
| Term | Value | Share |
|---|---|---|
| Potential energy released | 11,163 J | 100% |
| Kinetic energy at the finish | 7,800 J | 70% |
| Aerodynamic drag work | about 2,030 J | 60% of losses |
| Rolling and bearing losses | about 1,340 J | 40% of losses |
Your car will not match these numbers. The point of declaring them is that when you disagree with a conclusion below, you can find the number that carries it and substitute your own.
AIR DENSITY IS THE LARGEST THERMAL EFFECT
It is also the one you cannot tune, which is exactly why it has to be recorded.
Drag is proportional to air density, and air density is set by temperature, pressure, and humidity through the equation of state:
Fᴅ = ½ρCᴅAvᵣₑₗ²
Run the numbers on an ordinary race day. A cool 18 °C morning and a warm 30 °C afternoon differ by 12 kelvin on an absolute scale of about 293, which is a 4.0% density difference. On the reference run that removes about 81 J from a 2,030 J drag bill, or roughly 2.4% of everything the car loses. A 20 hPa change in barometric pressure moves density another 2%. Humid air is less dense than dry air, not more, because water vapour is lighter than the nitrogen and oxygen it displaces, and that is worth about another 1% on a hot, wet day.
Put together, the air a car races through can vary 3% to 5% in density between two sessions at the same track. That is several times larger than any finish, coating, or colour effect discussed anywhere on this page, and it arrives whether you thought about it or not.
What Formula 1 does with air temperature
This is the part of professional motorsport that genuinely transfers. Formula 1 teams treat ambient temperature and pressure as direct inputs to lap simulation, because a 3% density change is 3% of the downforce and 3% of the drag. High-altitude circuits are the extreme case: teams run near-maximum wing there purely to recover density that the thin air took away. Track temperature driving tyre thermal state is arguably their single largest performance variable.
What does not transfer: cooling-system drag, radiator exit sizing, and tyre blankets all belong to a car with an engine and a rule book that permits them. A gravity racer has no heat to reject and no permission to condition a tyre. The transferable lesson is narrower and more useful: professionals record the air before they trust a test result.
The practical consequence
You cannot buy thinner air, so density is not a tuning knob. It is a confound. If you time a baseline on a cool morning and the change on a warm afternoon, the weather moved the result by more than almost any legal modification you could have made, and the run sheet will credit your change for it. Record temperature, pressure, and humidity beside every timed run, keep A/B pairs inside the same weather window, and randomise the order within the pair.
WHEELS AND AXLES: THE THERMAL LEVER THAT IS ACTUALLY YOURS
Two mechanisms, both real, both requiring measurement rather than assumption.
If any thermal effect on a gravity car is worth a season of attention, it is the temperature of the rolling parts, because rolling and bearing losses are around 40% of the reference run's loss budget and both of their loss mechanisms are temperature-dependent.
MECHANISM ONE
Lubricant viscosity
Viscous drag in a bushing or bearing scales with the lubricant's viscosity, and viscosity falls steeply with temperature. For typical light oils it roughly halves over a 15 to 20 kelvin rise near room temperature. Warm running gear genuinely spins freer, and this is not a marginal dependence.
MECHANISM TWO
Wheel material hysteresis
A polymer wheel loses energy because it deflects and recovers imperfectly under load. That loss depends on the material's loss modulus, which is temperature-dependent, but not monotonically: warming can soften the wheel, enlarge the contact patch, and increase deflection loss instead of reducing it. Which way your compound goes is a measurement, not a deduction.
Tony Carlini Sr. reported exactly the first of these in Derby Tech in May 1984: a car with black axle trees radiates solar heat into the wheels and axles, and he measured slightly higher wheel and axle temperatures with slightly faster wheels as a result. That claim has aged far better than the article's aerodynamic argument, and it is the one worth re-testing on modern wheels.
Read the rule book before you condition anything. Whether you may deliberately warm, store, shade, blanket, or otherwise treat a wheel is a rules question, not a physics question, and wheel treatment is a controlled area in derby racing precisely because it affects speed. Your current ISBD or NDR rule book, your division plan, its amendments, and the inspector at your race decide what is permitted. A mechanism being real never makes an intervention legal.
THE SURFACE AND THE BOUNDARY LAYER
Derby Tech got the direction of this one backwards, and the correction matters more than the conclusion.
The thermal case for a black car was made by Tony Carlini Sr. in Derby Tech, May 1984, in an article called "Color Me Fast". He argued from Abbott and Von Doenhoff's Theory of Wing Sections and from Schlichting's Boundary Layer Theory rather than from pit lore, which is why the article deserves engagement rather than dismissal. His reasoning was that since heat leaving a surface destabilises laminar flow above Mach 2, the reverse must hold at 30 mph, so a sun-warmed surface should give a more stable boundary layer and less drag.
The inversion does not hold, and the standard low-speed result runs the other way. The reason is what temperature does to the viscosity of a gas. Air gets more viscous as it gets hotter. Set the pressure gradient to zero and evaluate the momentum equation at the wall, and the curvature of the velocity profile at a heated wall comes out as:
At a heated wall the temperature falls away from the surface, so (∂T/∂y)_w is negative; for a gas dμ/dT is positive; and the velocity gradient at the wall is positive. The product makes the wall curvature positive, which forces an inflection point into the velocity profile. By Rayleigh's criterion an inflectional profile is inviscidly unstable, so heating a surface in air moves transition earlier, in the same way an adverse pressure gradient does. Cooling the wall does the opposite and stabilises it.
Two things follow. First, the temperature ratio behind the article's quoted skin-friction figures, one quarter of free-stream absolute temperature, describes a wall near 73 K if the air is at 293 K. That is a cryogenic condition, and reading it across to a fibreglass shell in the Ohio sun is a gap of roughly 200 kelvin. Second, and more usefully: in a liquid the signs reverse, because liquid viscosity falls with temperature. Heated-surface drag reduction is a real concept for a hull in water. It is not one for a car in air, and the difference is the sign of dμ/dT rather than anything about speed.
The honest ending is that this cuts both ways and stays small. Earlier transition is not automatically slower on a real shell, because a turbulent boundary layer resists separation better than a laminar one, and a gravity racer is blunt enough for that to matter. The net sign on a specific body is genuinely uncertain, and the magnitude is a fraction of what the weather did to the air density that morning. Carlini's own measured answer for black over white was "about six inches", and he wrote plainly that "colour selection alone is not enough to make you win, but it helps". Both halves of that sentence are correct.
For context on how much heat a finish actually collects: in full sun a black shell sits perhaps 30 to 40 kelvin above ambient standing still, and roughly 15 kelvin above a white one once the car is moving at race speed and forced convection is carrying heat away. A thin composite shell has a thermal time constant near two minutes, so a car that heat-soaked in the staging lane keeps most of that heat through a 27-second run.
MYTHS, WITH THE NUMBERS THAT KILL THEM
Four from Derby Tech in 1984, and one that still circulates today.
The first four were listed by Carlini himself, because they were already circulating in the pits and none of them survived his testing. The fifth is the modern one and it is the reason this section carries arithmetic instead of assertions.
| The claim | Why it fails |
|---|---|
| A black car cooks the resin and fibreglass inside, costing resiliency | Softening those materials needs roughly 145 °F and up. Those temperatures are never reached inside a racer. |
| White front half, black back half, so cool air contracts ahead and hot air expands behind and pushes the car | Carlini: "It does not work on hill tests, wind tunnels, or anywhere." |
| A black car heats the surrounding air, thinning it so the car penetrates more easily | The car heats a boundary layer millimetres thick, not the air column it is about to drive into. Ambient density is set by the weather, and the weather moves it 3% to 5% while the shell moves it nowhere. |
| A white racer reflects heat onto the wheels and axles and speeds them up | Wheels and axles do run faster hot, but a white racer does not radiate enough heat to achieve it. Black axle trees are the mechanism that worked. |
| Hot air rising off the shell clears a path, so oncoming air only has to displace air that was already lifting away | Buoyancy is far too slow to do this. Numbers below. |
Why the rising-air argument fails, in three lines
Buoyancy is an acceleration, a = g·ΔT/T. For air 20 kelvin hotter than ambient that is 9.81 × 20/293 = 0.67 m/s². The only question left is how long it gets to act, which is how long a parcel of air spends on the car:
buoyant rise = ½ × 0.67 × 0.15² = 0.008 m (8 mm)
turbulent boundary layer at the tail ≈ 42 mm
Richardson number Ri = g·β·ΔT·L / v² ≈ 0.008
Eight millimetres of drift, inside a boundary layer five times thicker, and that assumes an implausibly uniform 20 kelvin excess across the whole layer. The Richardson number says buoyancy is contributing under 1% of what the forced flow is doing. In the car's own frame the hot air is not rising off the shell at all: it is being swept backwards at nearly 13 m/s while drifting upward at a fraction of a metre per second.
There is also a modelling error underneath the arithmetic. The picture treats the air near the shell as a resident volume that oncoming air must shoulder aside, and it is not one. A boundary layer is a continuous shear region in which the same air is being replaced constantly at close to free-stream speed. Nothing accumulates, so nothing needs evicting, so being "already on its way up" buys nothing. Analogies to two players contesting leverage import a moment arm that a fluid does not have.
The place this intuition is right is where buoyancy has time to work: thermals a glider circles in, a plume above a fire, air rising off a sunlit parking lot on a still day. Those are minutes and metres. A derby run is 0.15 seconds of contact per parcel of air.
TEST IT PROPERLY OR DO NOT CLAIM IT
A thermal effect is small enough that ordinary run-to-run spread will fake it in either direction.
Every effect on this page except air density is small enough to be invented by a sloppy test, and air density is large enough to fake all the others. That combination is why thermal claims have circulated unresolved in this sport for forty years. The protocol below is the minimum that separates a signal from a warm afternoon.
- Write the prediction first, including its direction and rough size, before the first run. A hypothesis formed after the data is not a test.
- Record the air on every run: temperature, barometric pressure, humidity, and wind speed with direction. Without these the run sheet cannot be reused next season and cannot be compared across sessions.
- Measure temperature rather than assuming it. An infrared thermometer on the shell, the axle trees, each wheel hub, and the track surface, taken at a marked spot and a marked time relative to the run, converts an argument into data.
- Pair and randomise. Run baseline and change alternately, reverse the order halfway, and keep both halves of every pair inside the same weather window and the same lane.
- Keep the wheels straight. Wheel IDs, positions, and the lane travel with every row, because wheel-to-wheel variation is larger than every thermal effect here except density.
- Compare the effect against the spread, not against a single fast run. If the difference is smaller than the ordinary variation between repeats of the same condition, the result is unresolved. Report it that way.
- Reverse it. An effect that disappears when the run order is flipped was drift, not physics.
Start a thermal run log in My Race Shop Return to the full Setup Lab workflow
BEFORE YOU PAINT, WARM, OR SHADE ANYTHING
Finish and wheel treatment are rules questions first and physics questions second.
Colour, coatings, films, waxes, tapes, surface treatments, and any deliberate conditioning of wheels or axles are governed by your current ISBD or NDR rule book, your division build plan, its amendments, and the inspector at your race. The Masters plan in particular controls surfaces and prohibits aerodynamic tape treatments outright. A thermal argument from 1984, or from this page, authorises nothing.
The child comes before the car. A dark shell left in the sun is a heat problem for the driver inside it long before it is an aerodynamic advantage. Check seat, shell, and helmet surface temperature by hand before the driver gets in, and keep both the racer and the car shaded until they are called. A shell that heat-soaked to 40 kelvin above ambient is not a setup decision, it is a burn risk and a heat-illness risk.
One further note on the source. The second half of "Color Me Fast" is about colour as psychological warfare against opponents and officials. That is period material, it is recorded in the Derby Tech archive for completeness, and it is not a claim this site endorses or repeats.
SOURCES & FURTHER READING
Check the primary material.
- Derby Tech, May 1984 - Newsletter for the Technical Enthusiast Primary source held as a photographed page set. Editor and publisher Ollie Brower, Newbury Park, California. Facts, measurements, and survey results are reported here with short attributed quotations; the issue itself remains under its own copyright and is not republished in full.
- Abbott and Von Doenhoff, Theory of Wing Sections The aerodynamics reference Derby Tech treated as standard reading. Cited in the May 1984 issue for skin friction and for the NACA 6-series profiles behind its airfoil data sheet.
- Schlichting, Boundary Layer Theory Cited by Tony Carlini Sr. in Derby Tech May 1984 for how surface-to-air heat transfer shifts laminar-to-turbulent transition.
- NASA Glenn: Equation of state Primary educational reference for the relationship between air pressure, density, and absolute temperature used here to size day-to-day density changes.
- NASA Glenn: Boundary layer Primary educational reference for the thin sheared layer next to a surface, laminar and turbulent states, and why transition location changes skin friction.
- NASA Glenn: Drag coefficient and the drag equation Primary educational reference for drag force, density, velocity, reference area, and drag coefficient. It explains physics, not Derby legality.
- NIST Engineering Statistics Handbook: What is experimental design? Primary guidance for planning controlled changes and measured responses so an experiment can support valid, objective conclusions.
- ISBD Masters build plans, July 2026 Current official build plan linked from the division hub. Use it directly; this site does not reproduce it.
- ISBD Rule Book - linked for the 2026 World Championship Official PDF currently linked from Race Week resources; the file itself says revised June 2025.