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Acceleration & Time-to-Speed

Top speed is the wrong number for a 12-foot field. This works out how long you actually take to get anywhere, and how much of your quoted speed you never see.

Inputs

The full size V5 motor. Most drivetrains are built from these.

The smaller V5 motor. It gives roughly half the torque, so two of them are worth about one of the big ones.

Diameter across the wheel. Mecanum and flex wheels share a diameter with the plain ones, so pick by name rather than by size. Anything not listed can be typed in.

lb

Caps how hard you can accelerate before the wheels spin.

Results

Time to cross the field

—sec

144 inches from a standstill.

If you ignored acceleration

—sec

Acceleration costs you

—%

Time to cross one tile

—sec

24 inches.

Time to reach 95% of top speed

—sec

Distance used getting there

—in

Top speed

—ft/s

Starting acceleration

—g

Race the robot that ignores it

Race the robot that ignores it
0 s

Two robots leave together on the same field. The top one is yours, working up to speed the way a real drive does. The bottom one is the arithmetic that only knows top speed, starting at full pace. Watch the gap open, and notice it never closes: the tenths lost getting going are gone for the rest of the run.

How this is calculated

A robot does not leave the line at its top speed. It builds up to it, and over twelve feet a surprising share of the run is spent still building. That is why two robots with the same quoted ft/s can be visibly different across a field.

Two forces, and the smaller one wins

At any instant the force pushing the robot forward is whichever of these is smaller:

from the motors F = (motors × stall torque × ratio ÷ radius) × (1 − v ÷ v_top) from the floor F = grip × weight

The motor term starts high and falls to zero as you approach top speed. That is the same torque curve as the stall calculator. The traction term is flat. So a strong drive usually spends its first moments traction-limited, wheels on the edge of slipping, then hands over to the motor curve as speed builds.

Why this is simulated rather than solved

Because the governing force switches between those two expressions partway through, there is no single tidy formula for the whole run. This page steps through the motion in half-millisecond intervals, recalculating force and speed each step, and reports where the robot actually was. That is both more honest and easier to check than an algebraic result that hides the switchover.

The part worth taking away

Compare the field crossing time with the naive figure. The gap is time you lose to physics that a top-speed number does not mention. It grows with a heavier robot, and it grows with a higher top speed. The faster the drive, the larger the share of the field spent getting there.

This is the real argument against chasing extreme gear ratios. Past a point, a higher top speed buys nothing over twelve feet because you never reach it, while the torque you gave up costs you on every start.

Sources & assumptions

Stall torque is published for the 100 RPM cartridge andderived for the others by inverse scaling with speed. Free speeds and wheel diameters are VEX published figures. The field is 144" square with 24" tiles.

The friction coefficient is estimated, since no VEX figure exists. It sets the traction ceiling, so it matters most in the first moments of the run and barely at all near top speed.

Uses a linear torque-speed curve and forward Euler integration at 0.5 ms steps, which is far finer than needed for the accuracy claimed here.

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

    Rough notes

    Rough notes

    Rough notes

    Rough notes

    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

                                Write it now

                                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

                                Drivetrain Speed Calculatorfills in your gear sizes herePushing Force & Traction Limitfills in your robot weight hereTipping & Wheelie Thresholdfills in your robot weight hereCenter of Gravity Locatorfills in your robot weight hereGear Ratio Solverfills in your cartridge here

                                You are here

                                Acceleration & Time-to-Speed

                                Where your answer goes

                                Autonomous Time Estimatoruse that speed and acceleration to time your whole autonbrings your acceleration with itTipping & Wheelie Thresholdcheck that launch does not pop the robot into a wheeliebrings your robot weight with itAutonomous Route Optimizerfind the quickest order of stops for a robot that accelerates this waybrings your acceleration with itMotor Current & Battery Budgetsee what hard starts cost in battery over a matchuses your motor count again

                                a number carries across the next question it raises

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