On the kart: the brake pedal, the steering arms, the tie rods, the engine mount adjuster, and the sprockets (a 72/20 ratio is a lever with a 3.6:1 arm). Every one of them trades distance for force.
The principle in one sentence
A lever trades distance for force in exact proportion: push the long end twice as far and the short end pushes twice as hard.
The one equation
force_out x arm_out = force_in x arm_inBoth sides are the same quantity, called torque: a force times the distance from the pivot at which it acts. Units: pounds x inches = lb-in (or lb-ft; 1 lb-ft = 12 lb-in). The lever doesn't create torque, it passes it through. Rearranged:
force_out = force_in x (arm_in / arm_out)The ratio arm_in / arm_out is the lever's multiplication. It's a pure number; the units cancel.
Math: ratios. A ratio is one number divided by another, and it tells you "how many times." arm_in / arm_out = 8 in / 2 in = 4 means the input arm is 4 times the output arm, so the output force is 4 times the input force. On a calculator: long arm divided by short arm. Ratios have no units when both numbers have the same unit - the inches cancel exactly like they did in lesson 1 - and here the ratio is simply how many times the lever multiplies your push.
Why it can't be free
Energy is force x distance. If the short end pushes 4 times harder, it must move 4 times less, or the lever would put out more energy than went in. That's the trade every force multiplier on this page and the next (hydraulics) makes: more force, less travel. There is no machine that gives you both.
On our kart, in numbers
The brake pedal. The pedal is a lever pivoted at its base. Your foot pushes at the pad, the brake rod pulls from a point lower down. Say the pad is 8 in from the pivot and the rod attaches 2 in from it (typical; measure ours). Pedal ratio = 8 / 2 = 4. Push with 50 lb and the rod pulls with 200 lb. Push the pad 1 in and the rod moves 1/4 in.
The sprockets. The chain pulls on the rear sprocket at its radius and on the driver at its radius. Radius is proportional to tooth count (same chain pitch), so the "arm ratio" is 72 / 20 = 3.6. That's why lesson 2 could say torque at the axle = engine torque x 3.6: it's a lever. The price, per the same rule: the axle turns 3.6 times slower than the engine.
The steering. The steering wheel is one lever (wheel radius to column), the steering arm on the spindle is another (arm length to the kingpin). Two levers in series multiply: total ratio = ratio_1 x ratio_2. A small wheel makes steering heavier because it shortens the first arm. This is why a steering wheel's diameter is a setup choice and not a style choice.
Two things to notice
- Levers in series multiply. Pedal (4:1) into hydraulics (next page, about 5:1) into the pad's friction: the multiplications stack. 50 lb at the foot can become 1000 lb squeezing the rotor. When something in that chain is loose or bent, the loss multiplies too.
- The arm is the perpendicular distance. Push along the lever instead of across it and the arm is zero: no torque, no matter how hard you push. That's why the brake rod should meet the pedal at a right angle at the point of max effort, and why a bent pedal feels weaker even though nothing is broken.
Problems
1. Measure the pedal. Tape measure on our kart: pivot to the center of the pedal pad, pivot to the brake-rod attachment. What is the pedal ratio? If the driver pushes with 60 lb, how many pounds does the rod pull?
2. Move the rod. The rod has two attachment holes on the pedal (typical). Moving it to the hole closer to the pivot: does the rod force go up or down, and does the pedal travel to the same stopping force get longer or shorter? Which would you want for a driver who brakes late and hard?
3. Steering weight. Our steering wheel is 300 mm across (typical; measure). Swapping to a 280 mm wheel changes the first lever's arm from 150 mm to 140 mm. By what factor does the effort at your hands change for the same force at the tires? (Ratio of the two arms, and which way.)
Go look: find the pedal pivot and the rod attachment, and the two holes. Then look at the steering arm on the spindle and find its pivot (the kingpin). Every lever on the kart has a pivot; finding it is the whole skill.