EDUKATE SINGAPORE · GOLD STANDARD PRACTICAL CASE STUDY 203
Ten correct wheel revolutions can produce the wrong travelling distance.
A school robot changes from 80 mm to 100 mm wheels but its encoder software retains the old distance conversion. This original case explains circumference, percentage comparisons, sensor evidence and why hardware changes need a new accepted performance test.
All robots, pupils and measured outcomes are fictional. VEX educational documentation explains underlying rotation and wheel mathematics, not a finding about any actual device.
The decision at a glance
- Original diameter: 80 mm.
- Replacement diameter: 100 mm.
- Rotation count: ten complete wheel revolutions.
- Old distance: approximately 2.513 m under ideal rolling.
- New ideal distance: approximately 3.142 m.
- Meaning: 25% farther than the old estimate; old estimate is 20% low relative to the new distance.
Chapter navigation
- 1. The robot’s distance display remains green after a wheel replacement
- 2. Counted rotations and actual ground distance answer different questions
- 3. The circle formula reveals exactly how much the distance changed
- 4. VEX explains how encoders become distance estimates
- 5. A high-resolution encoder does not compensate for an old wheel diameter
- 6. The immediate exhibition decision should use the tested service state
- 7. Hardware change needs a software-change handoff
- 8. Real driving adds wheel slip, surface and turning effects
- 9. Retest a wheel swap before the public demonstration
- 10. Practice: ten revolutions, two wheel sizes, one changing distance
1. The robot’s distance display remains green after a wheel replacement
A fictional Secondary 2 robotics team builds a small autonomous vehicle for a school exhibition. Its drive wheels originally measure 80 mm in diameter. A shaft-rotation sensor counts the wheels’ revolutions, and the controller converts that count into estimated ground distance. After calibration under the original configuration, the class can predict the vehicle’s travel on a straight test surface within its accepted conditions.
Before the exhibition, the students replace the worn drive wheels with a 100 mm diameter model. The software retains the earlier wheel-circumference constant. On the next controlled test, the motor completes ten revolutions and the display reports approximately 2.51 metres, just as it did before. The actual distance predicted from the new wheel diameter is approximately 3.14 metres if the wheel rolls without slip.
The Gold Standard problem is not that the encoder has necessarily failed. Its rotational count can be entirely correct. The distance estimate is wrong because a physical relationship used to interpret rotation has changed. A valid sensor count, a stored geometry value and the movement on the floor are distinct forms of evidence.
2. Counted rotations and actual ground distance answer different questions
The system record R1 contains sensor counts or shaft rotations. Record R2 contains the wheel diameter used in the distance calculation. R3 identifies any gearing relationship between the observed shaft and the driven wheel. R4 holds the tested surface and operating conditions; R5 records a trustworthy distance observation when the students conduct an authorised check.
R1 establishes rotation under the sensor’s configured method, not necessarily linear distance over a floor. A wheel’s radius or diameter determines its ideal rolling circumference. Wheel slip, mechanical compliance, gear ratios and unequal wheel sizes may change how well rotation predicts ground movement. The original exercise deliberately uses an ideal no-slip comparison so students can isolate the geometry error first.
An encoder with a high-resolution signal can measure the wrong quantity for a larger claim when its software interprets the signal using stale physical data. That is an evidence-chain issue: GS-R02 defines what a valid distance measure must represent and GS-R08 requires the output to match the actual supported claim.
3. The circle formula reveals exactly how much the distance changed
The original wheel diameter is 80 mm, or 0.080 m. Its ideal circumference is π × 0.080 = approximately 0.2513 m. Ten complete wheel revolutions correspond to 10 × 0.2513 = approximately 2.513 m under the no-slip, one-wheel-revolution-per-count assumption.
With 100 mm wheels, the circumference is π × 0.100 = approximately 0.3142 m. Ten revolutions correspond to approximately 3.142 m. The difference is 3.142 – 2.513 = 0.628 m. The new wheel circumference is 100/80 = 1.25 times the old circumference, so the robot travels 25% farther than the old geometry predicts for a given number of wheel revolutions.
Expressed relative to the new actual ideal distance, the old display understates the distance by approximately 20%, because 0.628 divided by 3.142 is 0.20. That difference between 25% farther relative to the old estimate and a 20% understatement relative to actual distance is an excellent mathematical lesson about denominators. Both statements can be true when their comparison bases are clear.
4. VEX explains how encoders become distance estimates
The official VEX Library explanation of optical shaft encoders describes counting sensor pulses to infer shaft rotations. It explicitly shows that the circumference of a wheel equals π times its diameter and that travelled distance can be calculated from circumference multiplied by the number of revolutions.
The same guidance notes that the robot programme must include wheel size information for the sensor to support a distance estimate. It also distinguishes motor or shaft rotations from ground movement and discusses slip as a reason why wheel-derived estimates may become inaccurate. That is authoritative educational robotics context, not proof that the fictional team used any particular VEX hardware or committed a real defect.
The Gold Standard applies the same principle to other machines: measurements require a current mapping from raw sensor output to the quantity people intend to use. A software value cannot remain valid after a component change merely because its previous calibration report was green.
5. A high-resolution encoder does not compensate for an old wheel diameter
One pupil argues that the encoder counts very precisely, so the 2.51 m display must be reliable. But precision in rotations does not determine the accuracy of the conversion to metres. The robot may have accurately counted ten revolutions and accurately multiplied by the wrong circumference constant.
Another pupil proposes changing the requested revolution count until the robot appears to stop at the intended floor line. That could improve one demonstration without correcting the model. On a different distance or surface, the error may reappear, and any hidden gear ratio or slip may produce another discrepancy.
The credible correction is to verify the changed hardware configuration and the full rotation-to-distance relationship. Where a distance estimate is needed for a physical action, a competent operator should verify it for the intended conditions rather than infer safety or positioning capability from an unexamined sensor display.
6. The immediate exhibition decision should use the tested service state
The robotics tutor preserves the original software, replacement-wheel specification, sensor counts and observed test results. The team stops claiming the original distance calibration remains valid after the wheel change. This need not cancel the entire exhibition. The responsible teacher decides which demonstration can proceed appropriately under the school’s equipment and student-safety rules.
The class should not publicly report that the encoder was defective without evidence. Its limited claim might remain correct: the sensor counted ten wheel revolutions. The stronger claim that the vehicle travelled precisely 2.51 metres is not supported by the altered physical configuration.
A bounded explanation can tell visitors that the robot’s wheel-based distance software is being recalibrated after a diameter change. Turning that issue into a hands-on lesson about circles, ratios and evidence may be more educational than hiding it behind a perfect-looking final display.
7. Hardware change needs a software-change handoff
The workshop team replaced the wheels because their grip was worn. The programming team maintained the control algorithm. Nobody had written a rule requiring the wheel diameter used in the calculations to be rechecked when parts change. Both teams could report their local work complete while the combined distance service remained unsuitable.
A useful configuration record identifies installed wheel diameter, relevant gear ratio, sensor origin, programme version, test surface and the accepted conditions of use. If a different student installs a new wheel, the software owner can see that the geometry assumption may need review. A checklist called ‘robot ready’ should not merely reflect a successful power-on test.
GS-R07 protects the handoff from mechanical work to software interpretation. GS-R12 protects future component changes. The principle is not to forbid substitutions; it is to prevent silent changes in what a sensor reading means.
8. Real driving adds wheel slip, surface and turning effects
The ideal circumference calculation assumes the wheel rolls without slipping. A robot making a sharp turn, moving on a smooth floor or climbing a small ramp may experience motion that does not correspond exactly to drive-wheel rotations. Tyre compression, tread differences and motor gearing can contribute further error.
The team should therefore distinguish a theoretical geometry result from measured performance under its actual operating conditions. A correct conversion constant improves the model but does not guarantee centimetre-level localisation over every path. Real movement may need suitable independent checks or additional sensing, depending on the task.
Students should learn the difference between model assumptions, measurements and deviations. A Gold Standard controller tells users what its distance estimate represents and where uncertainty remains; it does not disguise a conditional estimate as a universal ground-truth measurement.
9. Retest a wheel swap before the public demonstration
A controlled rehearsal begins with 80 mm wheels and a known rotation count. The team then changes to 100 mm wheels and asks whether the software detects or flags the changed geometry. An acceptance check must establish that the displayed distance follows the updated configuration rather than reusing the old wheel constant.
A second exercise varies the number of revolutions while preserving the new diameter, so students can see that the error grows with travelled distance. A third introduces a surface where slip is noticeable, helping reviewers distinguish a geometry problem from a real-world traction limitation.
The test should take place in an appropriate safe workspace, with the school controlling its equipment. The pass condition is a transparent, suitably verified distance estimate for the intended task, not a promise that every sensor-derived reading is exact.
10. Practice: ten revolutions, two wheel sizes, one changing distance
Exercise. A small robot is programmed using an 80 mm diameter wheel. Its sensor counts ten wheel revolutions. The team later installs 100 mm wheels but leaves the distance constant unchanged. Calculate the ideal old and new distances and explain which percentage comparison is being made.
The old estimate is 10π(0.080) = approximately 2.513 m. With the new wheels and no slip, the ideal distance is 10π(0.100) = approximately 3.142 m. That is 0.628 m farther, or 25% above the old estimate. The old displayed distance is 20% below the new ideal distance when the latter is the denominator.
The next acceptance test should verify the physical wheel identity, geometry value, sensor-to-wheel mapping and actual travelled distance before publishing a new performance claim. The Gold Standard lesson is that a perfectly accurate rotation count can produce a wrong distance when a physical assumption has silently changed.
Frequently asked questions
Did the encoder become faulty when the wheels changed?
Not necessarily. A correct rotation count can be converted using the wrong wheel circumference. Sensor operation and distance interpretation are separate questions.
Why is the robot said to travel 25% farther but the display is 20% too low?
The first percentage uses the old estimated distance as its denominator; the second uses the new actual ideal distance. Both are valid when clearly labelled.
Does the circumference formula guarantee exact driving distance?
No. It describes ideal rolling geometry. Slippage, gearing, tread deformation and actual surface conditions can affect movement.
Must the programme change after every hardware substitution?
At least the relevant configuration and assumptions need review. Whether software or calibration changes are required depends on what the component affects.
How can learners demonstrate the issue safely?
Use a controlled, suitably supervised test with known wheel sizes and measured travel, without assuming the estimate proves safety in uncontrolled environments.
Before the next robotics exhibition
- Identify the currently installed wheel model and diameter.
- Verify the sensor-to-wheel and gear relationships under the chosen configuration.
- Check the code’s physical conversion constant and units.
- Test actual movement on a suitable surface under the defined procedure.
- Record the limitation that slippage may change wheel-based estimates.
- Have the relevant school and technical owners accept the final service claim.
A further classroom investigation can hold the rotation count fixed while comparing different wheel sizes. Learners first predict a ratio using diameter alone and then confirm it by working with π and circumference. They should explain that the circumference ratio is the same as the diameter ratio, which is why the new ideal distance is 100/80 or 1.25 times the old ideal distance. This turns a technical maintenance problem into a direct mathematical demonstration of proportional reasoning.
An honest exhibition note could state that the encoder count was verified but the distance conversion required updating after the wheel change. The programme could still demonstrate the geometric model while clearly explaining that real movement depends on additional physical conditions. The Gold Standard purpose is not to make a robotics project look flawless. It is to make the relation between measurement, assumption and result understandable to students and visitors.
Wheel geometry and the command to travel one metre
The original drive programme contains an apparently harmless constant: the diameter of the installed wheel, multiplied by π to obtain circumference. During the first school test, this constant was checked and the robot stopped close to its intended line. After the class replaced its wheels, the sensor continued counting rotations while the code continued using the old diameter. Both parts were operating under their respective definitions, yet the integrated estimate no longer described the physical machine. A routine software test that supplies the old diameter again could pass without exposing the changed hardware. The release condition needs to connect the actual installed parts with the particular programme running at the exhibition.
Consider a command to travel exactly one metre in the simplified no-slip model. With 80 mm wheels, the controller would request 1 ÷ (π × 0.080), about 3.979 wheel revolutions. Under the same number of revolutions, 100 mm wheels ideally move the robot 3.979 × π × 0.100, approximately 1.25 metres. The machine would overshoot the original intended distance by about 0.25 metres. This is the same diameter-ratio effect as the ten-revolution case, but it presents the result from the perspective of a desired endpoint rather than a fixed rotation count. Students can see why an accurate motor command is not enough when geometry has changed.
Percentage language matters. Saying that the new distance is 25% greater compares 3.142 m with the old 2.513 m. Saying that the display is 20% short compares the missing 0.628 m with the actual 3.142 m. Both statements are mathematically compatible. A report that chooses the larger percentage simply because it sounds more dramatic has failed to explain the denominator. A tutor should show the base of each ratio, ask which question is being answered and then confirm the calculation. The same care prevents errors in retail discounts, examination marks and scientific performance comparisons.
The calculation assumes that encoder revolutions are the wheel’s own revolutions. If the sensor measures a motor shaft driving a reduction gearbox, the programme needs the proper ratio before multiplying by wheel circumference. For a simple fictional two-to-one relationship, twenty motor revolutions can represent ten wheel revolutions. Failing to identify the sensor location would cause another error even if the new wheel diameter were correctly entered. This case holds gearing constant to isolate the replacement wheels, but a full acceptance record should preserve the hardware arrangement that gives every rotation count its meaning.
Move from ideal geometry to a meaningful movement test
An appropriate school robotics test begins by identifying the wheel size and chosen sensor, then predicting travel for one, five and ten revolutions. With a 100 mm diameter wheel, ideal distances are approximately 0.314 m, 1.571 m and 3.142 m respectively. The old 80 mm conversion would display approximately 0.251 m, 1.257 m and 2.513 m. The absolute difference increases with movement, while the proportional error remains fixed under the ideal model. This gives students a practical opportunity to distinguish proportional reasoning from simple subtraction.
A relevant testing procedure uses a safely supervised space, an independent distance observation suitable for the expected precision, and a repeatable path. Students should record what was commanded, what the encoder counted, what distance the programme displayed and what the robot actually achieved. If their measuring tape or floor markers are not precise enough for a claimed centimetre-level result, they should report the limitation. A green test ought to mean that the observed outcome satisfies the defined requirement within understood uncertainty, not that the robot stopped near a marker on one visually pleasing run.
Turning introduces another subtlety. If a student replaces only one drive wheel, left and right diameters may differ. Equal encoder counts would then produce unequal ideal ground travel, making the vehicle turn rather than follow the straight line predicted by a symmetric model. A corrected average circumference does not automatically solve this asymmetric situation. The equipment and programme need to represent the actual arrangement. A synthetic simulation can teach this without pushing a student-built machine into an uncontrolled public area, and an authorised instructor can decide what physical demonstrations are suitable.
Wheel slip makes the evidence boundary even clearer. A motor can turn while the tyre momentarily loses traction, allowing encoder rotation without equivalent movement over the floor. The VEX optical encoder documentation discusses the distinction between drive-wheel rotation and an independent measuring wheel in cases where slip matters. That does not mean the fictional school must install extra hardware. It shows that geometric calibration and actual localisation accuracy are separate engineering tasks. A fully current wheel diameter improves the model but cannot guarantee perfect position across every surface, load and manoeuvre.
What a qualified reviewer should see before release
A useful configuration sheet links the approved robot version, installed wheel model, accepted diameter, gear ratio, sensor position, programme build and test conditions. A new wheel purchase should not close as a purely mechanical task if distance estimation uses the previous part’s dimensions. The relevant programming owner needs to review which constants or models may be affected. Conversely, a code change should not be reported as a physical correction until the installed robot is checked under its actual arrangement.
Suppose the students detect an observed travel of 2.95 m where the current ideal formula predicts 3.142 m. It would be premature to force the geometry constant smaller merely to fit that one result. The discrepancy may involve surface traction, wheel deformation, gearing, measurement accuracy or other conditions. A responsible review identifies possible causes, gathers suitable evidence and preserves the theoretical geometric calculation as distinct from empirical performance. A quick cosmetic edit to the display could produce a convincing final number while losing the relationship the model was meant to represent.
The centre’s dashboard can preserve a passing encoder-count check and a separate unresolved distance-estimation status. It should not erase a legitimate component achievement because an integration issue appears, but neither should it describe the whole robot as ready when an intended distance task remains unverified. The same evidence pattern recurs when a calibrated laboratory device is used with different accessories or a scientific figure is resized after a correct acquisition. The success of one step does not automatically transfer to changed downstream conditions.
The Clementi reference emphasises first principles, worked reasoning and checking rather than memorised answers. A robotics tutor can use the wheel swap to teach π, circumference, ratios, conversion of millimetres to metres and the meaning of the denominator in a percentage. Learners first calculate the result, then explain the assumptions, then compare it with a suitable observation. This sequence turns an equipment setback into a strong educational outcome rather than simply patching the programme until the demonstration appears to work.
Preserve a decision record another class can understand
The class should retain the old constant and the reason it was once correct, rather than silently replacing it and treating the previous result as a mystery. Its final report can state: ‘Ten measured wheel revolutions were processed using an 80 mm circumference model after 100 mm wheels were installed. The geometric conversion was therefore outdated; the new theoretical travel is 25% greater for the same revolutions before considering slip and other effects.’ That record identifies the observed input, missing assumption, corrected mathematics and remaining limitations.
A second teaching group should be able to read the configuration and reproduce the calculated ideal distance without needing to ask the student who wrote the software. That is a useful test of traceability. The group may choose a different practical measuring procedure, but it should be able to explain why the original model made sense and why it became unsuitable after the component change. The expected outcome is a shared understanding of how numbers describe real equipment, not a perfect score on a checklist.
The final exhibition can be honest and engaging. Students can show the two wheel sizes side by side, display the geometric predictions, compare ideal results with legitimate supervised observations and invite visitors to work out the 25% ratio. A Gold Standard demonstration does not conceal conditions under which performance varies. It gives viewers enough context to understand what the robot can do, what has been tested and which claims have deliberately been left open. That clarity is a stronger achievement than presenting a green distance label whose physical meaning nobody has checked.
Authoritative references and connected Gold Standard reading
- VEX Robotics · Using the Optical Shaft Encoder
- eduKate · Secondary 1 Mathematics Tutorials, Clementi Reference
- Gold Standard · Information and Record Integrity
- Gold Standard · Core Requirements and Evidence
- Case 147 · Calibrated Microscope and Incorrect Published Scale
- Case 170 · Pipette Calibration and Replacement Tips
- Gold Standard Casebook
GS-R01–GS-R12 is eduKate’s educational management framework and does not replace the equipment manufacturer’s operating guidance or the school’s safety procedures.