Driving & Travel
Math for getting from here to there
19 live exhibits. Each one already works. Change a number and see what happens.
Open as board Play with these together. Solving one grows related exhibits.
Arithmetic & Number SenseRoad trip math: miles, liters, and dollars
Convert once and the trip adds up: how far, how much fuel, how much money.
Linear EquationsSpeed, distance, time: how long is the drive?
Distance is speed times time. Rearrange it and you know when you’ll arrive.
Ratios & ProportionsE6B time and fuel: will it make it with a reserve?
Distance over groundspeed gives time; time times burn gives fuel. Then leave something in the tanks.
Linear EquationsE6B density altitude: the 120-feet-per-degree rule
Pressure altitude, plus 120 ft for every degree warmer than standard. Quick enough to do in your head.
Linear EquationsHooke’s law: how far does the car sag when you load it?
A spring squeezes in a straight line with the load: twice the weight, twice the sag, until it hits the stops.
Ratios & ProportionsTorque: how hard to pull the wrench, and what an adapter changes
Torque is force times distance. A longer handle takes less push, and an adapter that adds length means you must set the wrench lower.
Arithmetic & Number SenseE6B weight and balance: where the center of gravity lands
The CG is a weighted average. Load people, bags, and fuel, and watch the dot move in the envelope.
TrigonometryE6B descent planning: when to start down
A 3° path drops about 318 ft every nautical mile. Tangent turns that into a distance and a descent rate.
Ratios & ProportionsLead screw vs. ball screw: turning torque into a push
A screw trades turns for force: F = 2π × efficiency × torque ÷ lead. Friction decides whether it also holds the load with the power off.
VectorsCrossing a river: where you aim vs. where you end up
Your speed and the current add as arrows. Aim straight across and you drift; aim upstream and you can land right on target.
VectorsCrosswind landing: splitting the wind into two parts
Pilots break the wind into “along the runway” and “across it.” That’s vector math at 60 knots.
QuadraticsWing lift: why twice the speed means four times the lift
Lift grows with airspeed squared. Bernoulli, angle of attack, thin air, and the stall, all on one curve.
VectorsE6B wind triangle: heading and groundspeed
Point the nose into the wind just enough to track your course. Three vectors, one triangle.
Exponents & LogarithmsE6B density altitude, exact: standard atmosphere and humidity
The full standard-atmosphere formula, plus the dew point. Humid air is lighter, so it flies higher.
Exponents & LogarithmsE6B true airspeed: why you’re faster than the dial says
The airspeed indicator feels air pressure, not speed. Thin air at altitude makes true airspeed higher.
TrigonometryCrank and piston: turning rotation into back-and-forth
A crank turns a circle into a straight-line stroke. The connecting rod bends the motion away from a pure sine wave.
Linear EquationsDC motor torque–speed curve: where it runs, peaks, and stalls
Load a DC motor and its speed falls in a straight line to stall. Power peaks at half speed, and efficiency peaks at light load.
Calculus (intro)Speed from a position graph: the derivative
The steepness of a position graph is the speed. Shrink a secant line down to a tangent, and you have the derivative.
Calculus (intro)Distance from a speed graph: area under the curve
Speed times time is distance, one thin rectangle at a time. Add more rectangles and the total closes in on the exact area: the integral.