On the kart: between the engine crankshaft and the 20-tooth driver sprocket. The LO206 has no gearbox and no clutch pedal; this one device decides when the engine is connected to the axle. It's why the engine idles with the kart standing still, why the kart creeps as rpm rises, and part of why hairpin exit feels the way it does.
The principle in one sentence
Spinning weights fly outward harder the faster they spin, and above a set speed they fly out hard enough to grab the drum and drive it.
The one equation
F_out = m x omega^2 x rm is the mass of a clutch shoe, r is its distance from the center of rotation, omega is the rotation rate (radians per second: rpm x 2pi/60). F_out is the outward force the shoe pushes with. A spring holds the shoe in with a fixed force F_spring; the clutch engages at the rpm where F_out first exceeds F_spring.
Math: "goes as rpm squared." F_out depends on omega^2, omega times itself. Double the rpm and the outward force goes up 2 x 2 = 4 times; triple it, 9 times. The power tells you how sensitive the result is: a squared law is steep. On a calculator: omega, times itself, times m, times r. Physically, that's why a clutch goes from "not touching" to "locked solid" over a narrow band of rpm.
Math: radians and omega. A radian is an angle; one full turn is 2pi = 6.283 radians. omega = rpm x 6.283 / 60 turns "revolutions per minute" into "radians per second," which is what the equation wants. 3000 rpm = 314 rad/s. (Why physics uses radians: they make the v = r x omega relation exact with no constant in it.)
Math: centripetal force. Anything moving in a circle is being pulled toward the center; without that pull it would go straight. The pull needed is m x v^2 / r, or the same thing written with omega: m x omega^2 x r. On a calculator, with m in slugs (pounds / 32.2), r in feet and omega in rad/s, the answer comes out in pounds. The clutch shoe "feels" that pull as an outward push against whatever holds it in (the spring, then the drum). Same law as the cornering force in lesson 3: the kart in a corner is a shoe on a very large clutch.
Why it works
Below the engagement rpm, the spring wins: the shoes sit inboard, the drum is free, the engine spins alone. At engagement, the shoes touch the drum and friction (M03) starts passing torque. If the load on the axle is more than that torque, the shoes slip: engine turns, drum turns slower, and the difference is burned as heat in the lining. As rpm rises, F_out climbs with rpm^2, friction with it, until the clutch passes the full engine torque and locks; from then on it's a solid coupling. Engagement is not a switch; it's a ramp, and the shape of the ramp is the rpm^2 law.
On our kart, in numbers
All clutch internals below are (typical) for a stock LO206 clutch and should be treated as an illustration until ours is measured.
Engagement rpm. Shoe mass 0.15 lb (0.0047 slug), shoe radius 1.5 in (0.125 ft), spring holding force 57 lb. F_out at 3000 rpm: omega = 314 rad/s; 0.0047 x 314^2 x 0.125 = 57.5 lb. So engagement is about 3000 rpm. At 2000 rpm the shoe pushes 25.6 lb, well short; at 4000, 102 lb; at 6000, 230 lb: four times the 3000 value, per the square.
Where the hairpins put the engine. Lesson 9: minimum speed 30 mph in the hairpins, which on the 72 is 3330 rpm. That's only 330 rpm above engagement. The clutch is locked, but barely, and any lower minimum speed (a bobble, a slower corner, a tighter line) drops it into the slip zone: engine rpm holds up while the axle falls behind, which feels like the kart bogging and then catching. On the 73 the same speed is 3377 rpm: 47 rpm more margin, which is part of what a shorter gear "does" for hairpin exit that the torque math alone misses.
Slip heat. Engine at 3000 rpm making 8 lb-ft (typical), drum at 2000 rpm: the clutch passes torque across a 1000 rpm difference. Power burned = torque x slip rate = 8 lb-ft x 105 rad/s = 838 ft-lb/s = 1.5 hp, one BTU per second, into a lining the size of a matchbox. A second of slip is fine; a lap of slipping out of every hairpin cooks it, and a cooked lining has lower mu (M03), which makes it slip more.
Peak torque vs engagement. The engine makes its best torque near 4000 rpm (typical). Engagement at 3000 means the kart is connected 1000 rpm before the engine is strong. A clutch set to engage higher (stiffer springs) would let the engine rev into its torque before loading the axle: better launch, more heat, and in the LO206 world the clutch is governed by the Briggs rule set, so what's adjustable is whatever those rules say (typical: stock clutch, spring changes restricted). Check the rules before touching it; the reason other classes obsess over engagement rpm is exactly this trade.
Two things to notice
- The clutch is a friction machine driven by a squared law. M03's mu x N, where N comes from rpm^2. Two of the laws on this track, stacked.
- It hides the engine's weakness. Below engagement the engine is disconnected; in the slip zone it's partly connected. If hairpin exit feels lazy, the question is whether the engine is below peak torque (gearing) or the clutch is slipping (clutch). They feel similar and they're different fixes.
Problems
1. The square. Using the typical shoe (0.0047 slug at 0.125 ft), how many pounds does one shoe push outward at 1500 rpm, 3000 rpm and 6000 rpm? Check that the 6000 value is four times the 3000 value.
2. A stiffer spring. Replace the 57 lb spring with a 75 lb spring. At what rpm does the clutch now engage? (Set m x omega^2 x r = 75 and solve for omega: omega = sqrt(75 / (m x r)). "sqrt" is the square root, the number that times itself gives what's inside; it's the square-root key on a calculator. Then convert rad/s to rpm: times 60, divided by 6.283.) Is that engagement rpm closer to or further from the engine's peak torque at 4000?
3. The slow corner. Suppose a hairpin is taken at 25 mph instead of 30. On the 72, what engine rpm is that? (Lesson 2 Q2's conversion: mph x 63,360 / 60 gives in/min; divide by the 34.24 in tire circumference for tire rpm; times 3.6 for engine rpm.) Is it above or below the 3000 rpm engagement, and what does the driver feel on exit?
Go look: with the engine off, the clutch is the drum the chain's driver sprocket is mounted on. Spin the rear wheel by hand: the drum turns and the engine doesn't. That's the clutch disengaged. The shoes and springs are inside the drum.