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Catapult & Puncher Energy

How much energy your bands actually store, how much of it reaches the object, and how long the motors need to wind it back. The arm keeps more of that energy than most people expect.

Inputs

Type

in

How far the bands are pulled from their free length when cocked.

The object

oz
in

Pivot to the object at rest. This is the launch radius.

The moving parts

oz

The arm, or the slider. Whatever the bands accelerate besides the object.

in

Roughly 0.58 of arm length for an even arm pivoting at one end.

%

Bands lose real energy to heat and friction. Measure a shot and set this from the range you actually get.

Winding it back

in

Where the cocking force is applied. On a catapult that is how far down the arm the slip gear or string pulls. On a puncher it is the winch drum radius, usually an inch or less.

How far the driven gear rotates from fired to cocked. A slip gear is usually well under one turn.

Your measured band force

Same measurement as the band assistcalculator, and the same numbers work for both. Hang known weights fromone band and record how far it stretches.

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Results

Object leaves at

—ft/s

Band force data

—

Everything here depends on it.

Energy stored in the bands

—J

Reaching the object

—%

The arm keeps the rest.

Left in the moving mass

—J

Peak band force

—lb

Torque to cock it, against what the motors give—

Past the end of the bar it stalls before it is cocked, and no amount of waiting helps.

Torque needed to cock it

—lb·in

Time to wind back

—sec

At free speed. Under band load the motors turn slower, so the real cycle is longer than this.

How this is calculated

A catapult or puncher is an energy store with a trigger. The bands hold energy, the release hands it over, and how fast the object leaves depends on how much of that energy it actually receives.

stored energy = area under the force-stretch curve × number of bands

Note it is the area, not the peak force. Two setups with the same peak pull can store quite different amounts depending on the shape of the curve, which is another reason a single spring constant is no use here.

The arm keeps a share, and it is bigger than you think

On a catapult the bands accelerate the object and the arm. Both end up moving, so the stored energy splits between them:

E = ½·ω²·(I_arm + m_object·r²)

The share reaching the object is m·r² divided by that whole bracket. A heavy arm can swallow more than half the energy, so lightening the arm raises exit speed with no change to the bands at all. That is usually the cheapest improvement available, and it is invisible if you only think in terms of adding bands.

A puncher has the same problem in linear form: the slider mass competes with the object mass. Same fix, same reasoning.

Winding it back costs the same energy every time

The motors have to put back everything the bands released, against the peak force at full draw. That sets both the torque needed and the time, and it is why catapults are slow to cycle even when they launch hard.

The peak force also decides whether a slip gear can hold it. A cocking mechanism has to survive full draw force with the gearing you chose, which is worth checking against theshaft load check before it strips.

Efficiency is where the honesty goes

Real bands are lossy. They heat up, they have hysteresis, the release drags, and part of the energy goes into vibration and noise. That loss is not small and it is not predictable from published figures, so this page does not guess it.

Fire a shot, measure the range, work back through thelaunch studio to the exit speed you actually got, and set the efficiency figure from the ratio. Then the page is describing your mechanism rather than an idealised one.

Sources & assumptions

Stall torque is published for the 100 RPM cartridge andderived for the others. Gear tooth counts are VEX published sizes. Energy, rotational inertia and the energy split are standard mechanics.

Band energy comes entirely from your measurements. No spring constant is assumed anywhere, because rubber does not have a single one worth quoting.

Assumes the bands release all their stored energy over the full draw, the object leaves at the end of the stroke, and nothing binds. Real releases are messier. The efficiency figure is where that reality is meant to go, and it is yours to measure rather than mine to invent.

Radius of gyration is an estimate you supply. For an even arm pivoting at one end it is about 0.58 of its length; a tip-heavy arm is higher.

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.

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.