On the kart: the wheels (aluminum, by rule), the frame (steel tube), the axle (steel), the engine block (aluminum), the seat (fiberglass). Three metals, three densities, and a rulebook that only lets you use one of them on the wheels.
The principle in one sentence
Density is how much mass fits in a given volume, and it comes from two things: how heavy each atom is, and how much room each atom takes up.
The one equation
density = mass / volume units: g/cm^3 (grams per cubic centimeter)
magnesium 1.74 g/cm^3
aluminum 2.70 g/cm^3
steel 7.85 g/cm^3Aluminum is 1.55 times as dense as magnesium; steel is 2.9 times as dense as aluminum. Same-sized part, that many times the weight.
Math: "per" quantities and comparing by dividing. "Grams per cubic centimeter" means: take the mass, divide by the volume. Any "per" is a division. To compare two densities, divide one by the other on the calculator: 2.70 / 1.74 = 1.55. That number has no units (g/cm^3 over g/cm^3 cancels) and reads as "1.55 times." Subtracting tells you the gap; dividing tells you the ratio, and the ratio is what carries over to any size of part: an aluminum wheel is 1.55 times the weight of the same wheel in magnesium whether it's a kart wheel or a truck wheel.
Why it works: the atoms
A metal is atoms packed together like oranges in a crate. Density = (mass of one atom) / (space one atom takes up). Two facts, both real constants:
- A magnesium atom weighs 24.3 (atomic mass units); aluminum 27.0. Aluminum's atom is 11% heavier.
- A magnesium atom is bigger: radius about 160 pm vs 143 pm for aluminum (a picometer is a trillionth of a meter). 12% bigger radius means 1.12 x 1.12 x 1.12 = 1.40 times the volume, because volume goes as radius cubed: three lengths multiplied together (M10 explains powers in full).
Heavier atom AND smaller atom: 1.11 x 1.40 = 1.56, almost exactly the measured 1.55. Magnesium is lighter because its atoms are slightly lighter and noticeably bigger, so fewer grams fit in each cubic centimeter. Nothing more mysterious than that.
The part that surprises people: stiffness per pound is the same
Stiffness (how hard a material resists being bent or stretched) is called Young's modulus, E. Real constants, in gigapascals:
magnesium 45
aluminum 69
steel 200Steel is 4.4 times stiffer than magnesium. But divide stiffness by density:
magnesium 45 / 1.74 = 25.9
aluminum 69 / 2.70 = 25.6
steel 200 / 7.85 = 25.5The same number, within 2%. A steel part, an aluminum part and a magnesium part built to the same stiffness weigh about the same. This is one of the strangest coincidences in engineering and it's why "lighter metal" is never the whole story: what you gain in density you give back in stiffness, unless the shape lets you use the volume well (next page). The real reasons to pick one:
- Geometry. A less dense metal at the same weight gives you a bigger, fatter part. Fat tubes and thick wheels are stiffer for their weight (M10). That's the magnesium wheel's actual advantage: same weight, more metal in the right place.
- Cost, corrosion, fire. Magnesium is expensive, corrodes fast in salt air, and burns (it's what flares are made of). Aluminum is cheap, stable, and doesn't. CCKRA requires 5-inch aluminum wheels, which removes the cost race and the fire risk in one line.
- Fatigue and welding. A kart frame flexes every corner of every lap, for years, and it has to be welded. Steel tolerates that bending-forever life far better than aluminum, which cracks after enough cycles, and steel welds are forgiving. So the frame is steel: thin-walled (M10) to get the flex the chassis needs, and heavy enough that ballast is rarely a problem.
On our kart, in numbers
A wheel. An aluminum 5-inch kart wheel is about 1.6 lb (typical). The same wheel in magnesium would be 1.6 x 1.74 / 2.70 = 1.03 lb, so 0.57 lb saved per corner, 2.3 lb for four. Against a 360 lb minimum, that's 0.6% of the kart, and since the class minimum is fixed, it would come straight back as ballast. The point of light wheels is not weight on the scale: a lighter rim takes less of the engine's push to spin up out of every corner, and the saved pounds can be bolted on wherever the corner weights want them (problem 3).
The frame. 30 mm steel tubes (from the homologation form). The same tubes in aluminum, same wall, would weigh about a third as much and be a third as stiff: to get the stiffness back you'd fatten them, and then they'd crack at the welds after a season. Nobody builds sprint kart frames from aluminum for that reason, and CCKRA's rules say steel anyway.
Two things to notice
- "Light" means density, "strong" means something else, "stiff" is a third thing. People use all three as if they were one. The rule book cares about the first (and fire); the chassis cares about the third; the axle cares about all three.
- The weight you save is only real if the rules let you keep it. On a kart at the class minimum, every pound off the kart is a pound of lead bolted back on, and lead you can put where you want. That is the one legitimate reason to want lighter parts: choosing where the weight sits, not how much there is.
Problems
1. Weigh a wheel. Put one of our aluminum wheels (no tire) on the kitchen scale. How much would that exact wheel weigh in magnesium (multiply by 1.74 / 2.70)? In steel (7.85 / 2.70)?
2. Check the coincidence. Using the table, compute stiffness per density for all three metals yourself (E divided by density). What is the biggest difference between any two, as a percentage of the smallest?
3. Ballast. If you replaced all four wheels with magnesium and saved 2.3 lb, and the kart was exactly on the 360 lb minimum, how much lead would you have to add back? Where would you put it, and why does that make the swap worth something even though the scale reads the same?
Go look: find the stamp on the wheel rim (alloy wheels usually say what they are), the seam on the frame tube where the wall thickness shows at a cut end or a bracket, and the lead ballast on someone else's kart in the paddock. Ask them where they put it and why.