Online coding and Python classes in Solihull

When a system chases a new target at a rate proportional to how far away it is, its response follows a curve set by one number, the time constant. After one time constant it has covered 63 per cent of the gap, after about 2.3 time constants 90 per cent, and after about 4.6 time constants 99 per cent. The learner models an engine's power as exactly this kind of system. The time constants are invented for the lesson: 0.3 seconds for a nimble piston engine and 3 seconds for a turbine that has to spin up.

Ten times the time constant means ten times the wait, so in our model the turbine takes almost seven seconds to deliver 90 per cent of its power, against under a second for the piston engine. That gap is the heart of the problem the museum's record describes. The learner first uses the exact formula, then writes a loop that steps through time, nudging power towards the target a little at each step. With small steps the loop agrees with the formula; with half-second steps it reaches 90 per cent too early, a numerical error rather than a physical one.

Then the dangerous slip. If each step is longer than twice the time constant, the stepping method overshoots, swings below zero and grows wildly: with a 0.3 second time constant and 0.7 second steps our loop prints 2.33, then minus 0.78, then 3.37 and worse. Nothing physical does that; the program has become unstable. Learners add a check that refuses any step longer than twice the time constant. We also convert the record speed: 152 miles per hour is about 244.6 kilometres per hour, matching the museum's 244.

Never trusting a simulation until it passes a stability check is a habit a Solihull teenager picks up by coding in 2026. The longer argument is in why teenagers should still learn to code in 2026.