On the kart: three bearings on the rear axle (two in the frame hangers and the third-bearing support the rules require), two in each front wheel hub, one at each end of the steering column, and the clutch drum's needle bearing. Nine or ten places where a part turns against another part, and every one of them is a small tax on the engine's 8 horsepower.
The principle in one sentence
Rolling a hard ball over a hard surface takes a few thousandths of the force that sliding the same surfaces takes, so a bearing replaces sliding with rolling.
The one equation
drag force = mu x loadmu ("mew") is the friction coefficient: a pure number, the fraction of the load that shows up as resistance. Typical values:
steel sliding on steel, dry 0.5
steel sliding on steel, oiled 0.1
ball bearing, good, greased 0.002 - 0.005
ball bearing, dry / gritty 0.02 or worseMath: comparing very small numbers. 0.005 vs 0.5 is "a hundred times smaller": on the calculator, divide the big one by the small one, 0.5 / 0.005 = 100. When numbers differ by factors of ten, compare by dividing, not subtracting: the difference (0.495) tells you nothing useful, the ratio (100x) tells you everything. Engineers say "two orders of magnitude" for a factor of 100 (each order is a factor of 10). Physically, here: the same 205 lb of axle load produces 100 lb of drag if it slides and 1 lb if it rolls, and the bearing is the difference.
Why it works
Sliding: the two surfaces' microscopic bumps catch on each other and have to be torn or climbed over, continuously, along the whole contact. Rolling: a ball touches the race at one tiny spot, and that spot doesn't slide, it's set down and picked up, like a foot walking. Nothing gets dragged. The little friction that's left comes from the ball squashing slightly where it touches (the same hysteresis as a rubber tire, lesson 4's addendum, but in steel, so tiny), from the grease being pushed around, and from the seals rubbing. Wreck the grease with water or grit and the balls start to skid instead of roll, and the friction jumps toward the sliding number. That is what a "bad bearing" is.
On our kart, in numbers
Axle drag, good bearings. Rear axle carries about 57% of 360 lb = 205 lb across three bearings. At mu = 0.005: drag = 0.005 x 205 = 1.0 lb. At the wheel that's 1 lb of resistance, all lap long.
Axle drag, one bad bearing. Say one of the three goes gritty to mu = 0.05 on its share (~70 lb): 3.5 lb, plus the two good ones: about 4 lb total. Push the kart by hand and you'll feel the difference; the engine feels it too.
What a pound costs. Work = force x distance. 2 lb of extra drag over a 3643 ft lap is 7,300 ft-lb of energy per lap, which over a 58 s lap is 0.23 horsepower: 2.8% of an 8 hp engine, gone. Lesson 7 Q9 worked out that 0.1 g of drag (36 lb) costs 8.8 mph over a 4 s pull; scaling, 2 lb costs about 0.5 mph at the end of the straight, and a 20 lb dragging brake costs nearly 5 mph. The 9/19 main's late fade, if it had been a brake dragging, would have looked exactly like that.
The third bearing. With only two bearings, the axle is a beam held at two points and it bends between them under cornering load (M10 says how much: not a lot, but not zero). The third bearing, in the middle, stops the bend. CCKRA requires it (minimum 2 bolts) as a safety item; setup people also loosen or tighten it as a tuning item, because letting the axle bend a little changes how the inside rear lifts (lesson 13). Both uses are the same physics.
Two things to notice
- Bearings fail slow, then fast. A bearing losing its grease runs hotter, which thins the remaining grease, which loses more. It can be fine for a session and seized the next. Heat is the tell: a bearing housing warmer than its neighbor after a session is the early warning.
- Alignment is friction. Two axle bearings that aren't in line with each other load the balls sideways, which they hate. That's why the rear axle bearing hangers have slotted mounts and why "the axle should spin freely with the kart on the stand" is a real check, not a folk saying. Our hub-to-bearing measurements (4 7/8 in both sides) were the first step of exactly this check.
Problems
1. Spin test. Kart on the stand, give a rear wheel a firm spin and count seconds until it stops. Then do a front wheel. Which runs longer, and why should they differ (think about what each is dragging besides its bearings: chain and clutch on the rear, nothing on the front)?
2. Percent of the engine. If the rear axle's bearing drag rose from 1 lb to 4 lb (one bad bearing), how many extra ft-lb of work per lap is that, and what fraction of 8 hp does it eat over a 58 s lap? (1 hp = 550 ft-lb per second.)
3. Find the hot one. After a session, touch each rear bearing housing and each front hub in turn. If one is noticeably hotter, what are the two most likely causes (one is the bearing, one is not)? How would you tell them apart with the kart on the stand?
Go look: with the kart on the stand, spin the axle and listen: a good bearing is silent, a dry one hisses, a damaged one clicks. Find the third-bearing support and its two bolts (rule) and see whether it's snug or loose (setup). Feel the front hubs for side play by rocking the wheel top-to-bottom: play there is a bearing or a loose nut, and either one is a tech fail.