Model Railway & Scale Modelling Math: Scale Conversions, Scale Speed, Gradients & Helixes, Curve Radii, Track Plans and Fast-Clock Timetables

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Convert five real objects into model millimetres for four scale ratios, turn a model measurement back into real metres, work out the scale of an unknown model and round a model track gauge to one decimal.
• Turn six stopwatch runs into model speed and scale km/h, work out how many seconds the 200 cm straight should take at the branch-line limit and count the throttle steps that are too fast.
• Calculate the gradient of five ramps, check them against the club's fictional maximum, work out the height a planned ramp gains and the run needed so one track can cross over another.
• Compare five helix radii: track length per turn, gradient for the fixed rise per turn, the whole number of turns needed to reach the staging yard and the smallest radius that meets the fictional guideline.
• Look up the fictional guideline radius for each planned curve, label the curves that are too tight, calculate how far the middle of a long coach moves inward on a curve and count the curves that need a redesign.
• Calculate the arc length of a curve piece, collect the quantities per piece type from the segment list with SUMIF, and total the track length and the cost of the whole piece list.
• Work out the layout time at the end of a 90-minute session on a 4:1 fast clock, calculate arrival times, convert departures into real minutes after the start and write a departure-board line with TEXT.
• Add up the fictional current of all accessories, compare it with the usable part of a fictional supply rating, work out each category's share of the layout budget and show the cost plan in a chart.