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Lift Speed & Gear Ratio

How long a lift really takes under load, and which of the gear ratios that actually mesh gets it there quickest.

Inputs

The arm

lb
in
lb
in

The sweep

°
°

Used to show what a slower ratio costs you across a whole match.

The motors

%

A motor near stall gets hot. 60% is a reasonable ceiling for a lift that runs all match.

Results

Fastest ratio that works

—

It takes

—s

Working at

—% of stall

Free-speed guess would say

—s

That guess is optimistic by

—%

Torque needed, arm level

—lb·in

Ratios that work

—

Slowest working ratio costs

—s per match

How hard the winning ratio works the motors—

of stall torque, at the worst angle

Show the numbers behind this chart

Every gear pair that meshes on the hole grid, with what it can hold and how long it takes.

How this is calculated

Two things decide how fast a lift moves, and one of them is usually ignored. The first is gearing: reduce more and the output turns slower. The second is that a loaded motor is slower than an unloaded one, and how much slower depends on how hard it is working.

speed = free speed × (1 − torque used ÷ stall torque)

A motor at half its stall torque runs at about half its free speed. So a lift that is only just strong enough is not just marginal on force, it is also slow — and dividing the sweep by free speed misses that entirely.

Gravity changes through the sweep

The torque an arm needs falls with the cosine of its angle: hardest when level, easiest when vertical. So the motor is working hardest, and therefore moving slowest, at the bottom of the lift — and it speeds up as it rises.

That is why this page integrates across the sweep rather than using one average. Averaging the speed at the two ends gets the answer wrong in the direction that flatters the design.

The fastest ratio is the lightest one that holds

This is the part that surprises people. The instinct is to gear down for torque, and every step of extra reduction feels safer. But torque you never use is speed you gave away, and you pay for it on every cycle of every match.

So the search here does not look for the strongest ratio. It looks for the quickest one that still clears the load with the margin you asked for, and it shows what the over-geared alternatives cost you across a match.

Only ratios that mesh

VEX gears sit on a half-inch hole grid, and two gears only mesh if their tooth counts come from the same family — 12, 36, 60 and 84 in one, 24, 48 and 72 in the other. A 12:24 reduction looks tidy on paper and cannot be built on standard holes.

The table below only lists pairs that actually mesh, which is why some obvious-looking ratios are missing from it.

What this does not model

  • Acceleration. The arm has to be spun up, and on a short sweep that is a real fraction of the time. This gives the steady-state answer, so treat it as optimistic by a little even after the load correction.
  • Heat. The stall fraction tells you how hard the motors work, but not how they behave twenty cycles in. A lift at 70% of stall will be slower late in a match than the number here.
  • Current limiting. A V5 motor's controller intervenes near stall, so behaviour up there departs from the straight line this model assumes. That is another reason not to design above about 60%.

Save this as evidence

Collects what you entered, what came out, how it was worked out, and anything the tool flagged, with a timestamp and a version so someone else can reproduce it.

This is evidence, not a notebook entry. It deliberately does not write your problem statement, your reasoning, or your conclusion, because under RECF rules an Engineering Notebook has to be the students' own work and no tool may generate or organise its content. Take the numbers, decide what matters, and write it yourself.

Save this run, and compare

Keeps what is on screen so you can change something and see both sides of the change. Saved in this browser only, never uploaded.

Sources & assumptions

Cartridge free speeds and stall torques are VEX figures. The gear families follow from the half-inch hole spacing, the same rule the gear spacing tool uses.

The straight-line relationship between torque and speed is the standard model for a brushed DC motor, and is the reason a stalled motor turns not at all while an unloaded one turns fastest. It is a model, not a measurement: a V5 motor's own controller bends the line near stall.