Two 2-speed gearboxes in a row give four lever positions, but often only three different speeds. Gearboxes in a row multiply their ratios, and when both boxes use the same pair of ratios, slow + fast and fast + slow multiply to the same answer. The Three-Speed Car is built exactly this way, so it has a 9 : 1 crawler gear, a 3 : 1 middle gear and a 1 : 1 top gear, with the middle one reachable two ways. Real trucks avoid the repeat by making the second box's ratio different, and how different decides whether it is called a range box or a splitter.
The car: two little boxes, one behind the other
The Three-Speed Car is a level 4 build that takes about 60 minutes. Its build page lists the Clutch-Gear 2-Speed Car as the one to do first, because the Three-Speed Car is two of that gearbox joined end to end.
- An L motor drives the input shaft through a pair of corner gears.
- Main box (lever 1). On the input shaft sit an 8-tooth gear and a 16-tooth gear. They mesh with a 24-tooth and a 16-tooth clutch gear on the middle shaft, and a driving ring between them grabs one or the other. Slow is 8 driving 24, which is 3 : 1. Fast is 16 driving 16, which is 1 : 1.
- Range box (lever 2). The middle shaft also carries an 8 and a 16, and they drive the same pair of clutch gears on the back axle. So the second box is a copy of the first: 3 : 1 or 1 : 1.
The booklet points out why the gears fit: every shaft is 2 holes from the next, and 8 + 24 = 16 + 16 = 32 teeth. That spacing rule has its own explainer.
The middle shaft is doing two jobs at once. It is the output of the first box and the input of the second, which is why the ratios multiply, the same way stages do in compound gears.
Four lever positions, three speeds
| Lever 1 | Lever 2 | Overall | Wheel speed |
|---|---|---|---|
| slow | slow | 9 : 1 | 11% of top |
| slow | fast | 3 : 1 | 33% |
| fast | slow | 3 : 1 | 33% |
| fast | fast | 1 : 1 | 100% |
The percentages are ideal ratios. A real car slows a little more in the low gears because the motor is working harder, so a timed run won't match exactly. Ideally the turning force at the wheels goes up by the same factor the speed goes down, which is why the booklet's ramp challenge is for the 9 : 1 crawler gear. If torque is new to you, start with speed vs strength.
Predict the speeds
The lab keeps the car's main box and lets you swap the range box for two what-if ratios. Predict first, then check the chart.
Interactive: Range box lab. The Three-Speed Car’s two 2-speed boxes in a row: change the range box’s ratio and predict how many different speeds four lever positions give, the slowest crawler gear, and which ratio spaces the speeds evenly like a truck’s range box. Five challenges.
Two of the what-ifs answer the question real gearbox designers ask: if you add a second box, what ratio should it have?
How trucks use the same idea
Heavy trucks often put a small 2-speed box behind the main gearbox, and drivers' guides describe two kinds.
Range box. Its ratio is big enough that every high-range gear sits above every low-range one. With the range in low, you drive through the main box's gears; flick to high and the same gear lever positions give a whole new set of faster gears. Truck drivers call a 4-speed box with a range change "4 over 4": gears 1 to 4 in low range, 5 to 8 in high. In the lab, a 9 : 1 range box behind the 3 : 1 main box does this: 27, 9, 3 and 1 : 1, each step exactly 3 times the next, with no repeats.
Splitter. Its ratio is small. Instead of a new set of gears, it gives every main gear a slightly lower and a slightly higher version, so the engine speed changes by about half the usual amount when you shift. Drivers call it "half a gear". In the lab, the 5 : 3 what-if acts like a rough splitter: 5, 3, 1.67 and 1 : 1, four speeds in smaller, slightly uneven steps.
Big trucks often have both. One guide to an 18-speed truck gearbox describes a 5-speed main box whose range selector gives 9 ratios in all, and a splitter that doubles them to 18.
The Three-Speed Car is neither kind, because its second box copies the first. That is a feature for a learning build: the repeat at 3 : 1 is the surprise that makes the multiplying visible.
A speed chart to run
The booklet's own playtime idea makes a good fair test:
- Mark a 2-metre track on the floor.
- Time the car over it in all four lever positions, three runs each, using fresh batteries throughout.
- Find the two positions that give the same time. Then compare the 9 : 1 time with the 1 : 1 time: is it 9 times longer, or a bit more?
For the method behind fair gearbox tests, the two-speed gearbox test walks through one with a single box. For what the driving rings and clutch gears are doing inside, see the gearbox and clutch pages.
Interactive: Check yourself. A few quick questions on the ideas in this guide, each with an explanation.
- A 3 : 1 box drives another 3 : 1 box. What is the overall reduction?
- Why does the Three-Speed Car have three speeds and not four?
- A truck’s main box has a few gears. What does a range box behind it do?
- And a splitter?
