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Practice sheet · Aviation Path · Lens 1: Math

Speed, wind & trig

Practice for The Math of Aviation: knots, headings, chart scale, wind vectors, crosswinds, glide slopes, fuel and lift (pp.8–16), plus Algebra A1–A2 (pp.17–18).
Warm-upCoreLevel Up
Name Date Time I spent
Remember

1 knot = 1 nautical mile an hour; 1 nm = 1.852 km. time = distance ÷ speed. Reciprocal heading: add or subtract 180°. Wind and airspeed at right angles: use Pythagoras.

Crosswind = wind × sin θ; headwind = wind × cos θ (calculator in degrees). A 3° glide slope drops about 318 ft per nm. Avgas ≈ 0.72 kg per litre.

Warm-up

One step

Speed, headings, scale and temperature.
1

Trip time

A plane flies 250 nm at 125 kt over the ground. How long does it take? What is 125 kt in km/h?

2

Other end

Runway 07 points about 070°. What heading is the other end, and what is its runway number?

3

Chart scale

A line on a 1 : 500,000 chart is 9 cm long. How far is that on the ground?

4

Colder up high

It is 12 °C at sea level. Using 2 °C per 1,000 ft, about how warm is it at 4,000 ft?

Core

Two or three steps

Sketch the triangle before you calculate.
5

Dog-leg

A route goes 60 km north, then 80 km east. How long is the direct line? How much shorter is it?

6

Wind triangle

Airspeed 90 kt north; the wind pushes 30 kt east. Find the ground speed and the drift angle east of north.

Aviation Practice · Aviation Path · Unizon1/2
Aviation Path · Unizon · PracticeSpeed, wind & trigonometry
7

Crosswind check

Wind 25 kt blows at 40° to the runway. Find the crosswind and headwind. Is it within a 15 kt crosswind limit?

8

Coming down

On a 3° slope, about how high should a plane be 5 nm out? A plane that glides 10 : 1 is 800 m up: how far can it reach?

9

Fuel load

What is the mass of 120 L of avgas? A plane can carry 320 kg of people, bags and fuel. Two adults weigh 150 kg and bags 30 kg. How many litres can it take?

10

Square law

Lift grows with speed². By what factor does lift change if speed rises 20%? If it drops 20%?

Level Up

Equations

A1–A2 (pp.17–18).
11

Reserve

A plane starts with 180 L and burns 36 L/h (made-up): F = 180 − 36t. When does it reach a 30-minute reserve of 18 L?

12

Same height

Plane A: h = 2,000 + 400t. Plane B: h = 8,000 − 600t (ft, t in minutes). When are they at the same height, and what height?

13

Takeoff roll

A plane accelerates at 2.5 m/s² from rest: d = 1.25t². How long does a 500 m roll take?

14

Hangar

A hangar is 8 m longer than it is wide, with an area of 240 m². Solve w(w + 8) = 240.

Make your own problem

Your turn to be the flight planner

  1. Pick two Alberta airports or towns on a map.
  2. Write a question about distance, time, wind or fuel for the trip.
  3. Solve it, and add a reserve: what could change on the day?

My problem, and my worked answer:

Aviation Practice · Aviation Path · Unizon2/2
Aviation Path · Unizon · PracticeSpeed, wind & trigonometry

Try every problem first, then check here. Wrong answers are useful: find the step where your work and the key split apart.

The key never prints with Print my work or Print blank. Open it to get its own Print the answer key button.

Answer key

Worked solutions. Aircraft numbers are made-up examples, not for real flight planning.

Warm-up
1
2 h · ≈ 231.5 km/h 250 ÷ 125 = 2. 125 × 1.852 ≈ 231.5.
2
250° · Runway 25 70 + 180 = 250. Divide by 10: 25.
3
45 km 1 cm = 5 km. 9 × 5 = 45 km.
4
about 4 °C 4,000 ft is 4 lots of 1,000: 12 − 2 × 4 = 4. Real days differ from the standard.
Core
5
100 km · 40 km shorter √(60² + 80²) = 100. The dog-leg is 140 km.
6
≈ 94.9 kt · ≈ 18.4° √(90² + 30²) = √9,000 ≈ 94.9. tan⁻¹(30 ÷ 90) ≈ 18.4° east of north.
7
≈ 16.1 kt cross · ≈ 19.2 kt head · no 25 × sin 40° ≈ 16.1; 25 × cos 40° ≈ 19.2. 16.1 kt is over the 15 kt limit: choose another runway or wait.
8
≈ 1,590 ft · 8 km 5 × 318 = 1,590 ft. 10 × 800 m = 8,000 m (less into a headwind).
9
86.4 kg · 194 L 120 × 0.72 = 86.4. 320 − 150 − 30 = 140 kg; 140 ÷ 0.72 ≈ 194.4, so 194 L at most (round down for weight limits).
10
× 1.44 · × 0.64 1.2² = 1.44 (44% more). 0.8² = 0.64 (36% less).
Level Up
11
4.5 h 180 − 36t = 18 → 36t = 162 → t = 4.5. Canadian rules require a reserve like this (p.17).
12
6 min · 4,400 ft 2,000 + 400t = 8,000 − 600t → 1,000t = 6,000 → t = 6. Air traffic control keeps them apart.
13
20 s 1.25t² = 500 → t² = 400 → t = 20 (not −20).
14
12 m × 20 m w² + 8w − 240 = 0 → (w + 20)(w − 12) = 0 → w = 12.
Make your own: sketch the triangle, label knots, nm, ft and kg, and round fuel down when it’s a weight limit.
Aviation Practice · Aviation Path · UnizonAnswer key