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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.

1
2
3
4
5

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.

Pull the bands back

Pull the bands backstretch, inforce, lb
100%

Your band readings, force against stretch (the page starts with placeholder ones until you enter yours), with a dot for each one you measured. The energy stored in the bands is the shaded area under the line, up to how far you pull them. Pull further and the area grows faster than the stretch does, because the band is pulling harder at the end. Past your last reading the line is dashed: the page carries it on straight, and a measurement there would be better.

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.

Every source the site uses, and when it was checked

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.

Make a notebook page

Turns this calculation into a dated engineering notebook page: the setup, data, results, figures, working and sources, numbered and cited. You add the goal, the decision and the reflection in your own words, plus photos and sketches. Print it, paste it into Google Docs, or download a Word file or slides.

My notebook

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    Our own layouts

    A layout remembers how a page is set up: its type, its system, which parts print and which of your tables it uses. It never remembers a word, a number or a photo.

    Your team kept on this device
    Add someone to the team list
    Your words never written for you

    These are the parts a judge or teacher reads to see your thinking, so the page leaves them to you. Leave a box empty to get lined space for writing by hand. Start lines with "- " for a list. The notes under each box only count and point things out; they never change what you wrote.

    Rough notes

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    Rough notes

    Rough notes

    Rough notes

    Rough notes

    The word counts can be measured against a target your team sets on My notebook. The reading level is Flesch-Kincaid grade level = 0.39 × (words ÷ sentences) + 11.8 × (syllables ÷ words) − 15.59. Syllables are counted by vowel groups, so the grade is an estimate of the school year the writing reads at. It says nothing about whether the writing is any good.

    One part at a time, with a clock. At the end of practice, while you remember it.
    How you tested your details

    Fill in what applies. These print as a small table under the method.

    Before and after

    Compare this calculation with a run you saved earlier on this tool (under “Saved runs”). The page shows what changed and by how much.

    A line through the data from your recorded table

    Pick two measured columns from the same table. The page plots them and draws the least-squares line, only across the range you measured.

    Robot log a CSV from the robot's SD card

    Load a CSV your robot saved. Pick the time column and up to three columns to plot, and type their units. Only those columns go on the page; the file stays on this device.

    Two versions' trials your data, compared

    Pick a column of recorded trials for each version, from this page or another saved page. The page shows both averages and a 95% range for the difference. The numbers are copied in when you pick them, so later changes to the other page don't change this one.

    Options compared your scores

    Score each option 1 to 5 on each criterion, and weight each criterion 1 to 5 by how much it matters. The page only multiplies and adds.

    Photos and sketches stay on this device

    Up to 4. Paste a screenshot with Ctrl+V, drop pictures here, or pick them. Photos are shrunk before they’re kept, and an unsaved page keeps them in its draft. Use Mark up to draw arrows, labels, dimensions and numbered callouts on a photo. Mark one photo Before and one After to print them side by side.

      Test plan written before testing

      Write this before you test: the question, what you expect with a number, and what result would make you drop the idea.

        Build steps our build

        One row per step, in order, so someone could rebuild from this page.

          Parts used our parts list

          Lengths in holes are also shown in inches between the end holes. Weights are only added up where you type them.

            Plan the cuts: packs every piece of one part (sizes in holes, or inches on the hole grid) onto whole sticks of the stock length you type.

            Ways it could fail our scores

            List the ways this could fail. Score how likely (1 to 5) and how bad (1 to 5); the page multiplies them and puts the biggest risks first.

              Designed against built our measurements

              What the CAD or the plan said, and what you measured on the robot. The tolerance is yours.

                Changes from the last version our changes

                What changed since the last version, why, and which result it was meant to move.

                  That page’s settings, results and first photo are copied in and set beside this page’s. The result each change should move is looked up on both pages.

                  Tasks our plan

                  What needs doing, who, and by when. Open tasks carry to the next meeting page until someone ticks them done.

                    The pages behind this idea our evidence

                    The pages in this notebook that show the idea being tried, measured or changed. A judge reading the claim can turn straight to them.

                      Time spent our hours

                      Who worked on this and for how long.

                        Session log what we did, as we did it

                        Notes taken during a session. The time comes from the clock when the note was taken; every word is yours.

                          Size limit does it fit?

                          Type the starting size limit from the current game manual, and the robot's size as designed or measured, in inches. The site doesn't store the limit, because it changes with the game.

                          What broke from your breakage log

                          The breakage log is on My notebook. Copy it onto this page as a table, as it stands now; later entries don't change this page.

                          CAD model which version this page is about

                          Paste a link to the model (Onshape, Fusion or anything else) and the name you use for this version. For Onshape, the page reads from the link whether it points at a saved version or a workspace that keeps changing. Nothing is fetched.

                          Your code
                          Comments notes for the team, not the page

                          A teammate or coach can leave a note here. Comments stay beside the page, travel with it in exports and links, and don't print unless you tick them under Include.

                            Sources you used besides this tool

                            Videos, other teams, manuals, people. The tool’s own sources are cited for you.

                              Sign-off
                              Include

                              Press a ? to see what an option is for, or read them all on How the notebook tools work.

                              What “The calculator’s figures” is for

                              The calculator’s own diagrams and charts, numbered as figures and drawn from your numbers. Judges look for pictures that explain a design.

                              What “How it was calculated” is for

                              The formulas and steps the calculator used, so a reader can check the arithmetic for themselves.

                              What “The calculator’s warnings” is for

                              Things the calculator flagged, such as a motor near stall. They’re quoted and credited to the calculator, so they never read as your conclusion.

                              What “The calculator’s notes” is for

                              The calculator’s plain-language notes on the result. Off at first, because they read like conclusions, and the conclusions on a page should be yours.

                              What “Lined space” is for

                              Ruled lines under any part you haven’t written yet, so a printed page can be finished by hand.

                              What “Writing space as” is for

                              The blank space for handwriting as ruled lines, a dot grid or quarter-inch squares. Dots and squares suit sketches and hand-drawn graphs.

                              What “A summary under recorded data” is for

                              The number of readings, the average, the spread, the lowest and the highest under each table you recorded, worked out from your numbers. It shows every run counted, not just the best one.

                              What “Words used” is for

                              A small box with the site’s one-line definitions of glossary terms the calculator used, for readers who don’t know them. It never looks at your own writing.

                              What “Robot at the time” is for

                              The Robot Profile as it was when the page was first saved, so weeks later you can tell which version of the robot a test was run on.

                              What “Long tables in full” is for

                              Long calculated tables printed complete on an extra page, instead of every few rows on the page itself.

                              What “Fit on one sheet” is for

                              Smaller type and shorter tables, aiming for one printed sheet. Use it when every entry in your notebook should be a single page.

                              What “Wider left margin” is for

                              A wider left edge, so the page can be hole-punched or bound without losing any words.

                              What “Larger type, for reading aloud” is for

                              Bigger print with more room between lines, for the team member who reads the page to a judge. It overrides Fit on one sheet.

                              What “Our rubric scores” is for

                              Your own scores against the rubric, on a sheet of their own, for checking a page before a judge does.

                              What “When this page was first saved” is for

                              The day the page was first saved, printed beside its date. It shows the notebook was kept while the work happened.

                              What “Teammates’ comments” is for

                              Prints the comments teammates left on this page at the end, marked as not part of the page. Off at first, because comments are notes for the team, not for judges.

                              What “Show every table and block” is for

                              Shows every table and block in the editor, not only the ones this type of page usually uses. It changes the editor, not the printed page.

                              Rubric check

                                This checks what is on the page, not how good it is. Clear, specific writing in your own words is what earns the top marks.

                                Preview, letter size

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                                Where this goes next

                                Explore further on the full map

                                Where the answers on this page can be used, and which tools could have given you the numbers it asks for.

                                Comes after

                                Shooter Type Comparatorfills in your motor count hereRubber Band Assist Calculatorgives you your rubber band forceProjectile & Launch Studio

                                You are here

                                Catapult & Puncher Energy

                                Where your answer goes

                                Projectile & Launch Studiocheck that launch speed actually carries the object into the goalbrings your exit velocity with itShaft & Structure Load Checkcheck the shaft survives winding back and the snap of every shotbrings your gear sizes with itShooter Type Comparatorsee if a flywheel could fire faster than your wind-back timebrings your exit velocity with itShaft Deflectionsee how far the pull of the bands bends the pivot shaft

                                a number carries across the next question it raises

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