🏔️ Grade, Climb & Descent Calculator

What a grade actually means in degrees and feet, how fast your truck can hold it, and — the part that ends careers — how much heat a descent puts into your brakes, whether your retarder can carry it, and the descent speed it can hold without the service brakes.

Truck and grade
Continuous braking power it can absorb
Defaults: 80,000 lb gross, 450 hp, a 400 hp retarder, coming down a 6% grade at 35 mph.
The physics, in plain words

A grade of p percent is a rise of p per 100 travelled: 6% is 1 in 16.7, 3.43°, and 317 feet of climb in a mile. Climbing, the engine has to beat rolling resistance, air drag and gravity; descending, gravity does the work and something else has to get rid of the energy:

climb speed: P = v × ( m·g·Crr + m·g·sinθ + ½ρ·CdA·v² )
braking power: Pbrake = v × ( m·g·sinθ − m·g·Crr − ½ρ·CdA·v² )

The climb equation has no tidy closed form (v appears cubed), so it is solved by bisection here. Air drag rises with the square of speed, which is why a loaded truck runs out of puff on a grade so quickly, and why an empty one flies up the same hill.

The descent is an energy problem. Dropping 80,000 lb by 317 feet releases about 34 megajoules — close to the energy in a litre of diesel, every single mile. Nothing makes that energy disappear; service brakes turn it into heat in the drums and rotors, and if the heat arrives faster than the metal can shed it, the friction drops and the pedal goes soft. That is fade, and it is why the CDL manual's instruction is to come down in the same gear you went up in, with the retarder on and the service brakes used in short, firm applications rather than ridden.

Assumptions used above, so you can argue with them: rolling resistance Crr 0.0065 (a loaded tractor-trailer on good asphalt), air density 1.225 kg/m³ at sea level, drag area CdA 5.4 m² (a typical loaded tractor-trailer), 90% of engine power reaching the wheels, and steel brakes with a specific heat of 490 J/kg·K. Drum brakes are usually rated to work hard up to around 300–400°C; beyond that, friction falls off.

Retarder ratings are continuous-power figures at a stated temperature; a retarder running at its limit for mile after mile is a different animal from one used for ten seconds. Start the descent slower than you think you need to.