STEM LEARNING:

Advanced Air Mobility: Flight 

Control Math 4 (Pythagorean 

Theorem) Student Guide

www.nasa.gov

National Aeronautics and Space Administration
2 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 4 (PYTHAGOREAN THEOREM) STUDENT GUIDE

UAVS AND WEATHER

NASA is leading the nation to quickly open a new era in air 

travel called Advanced Air Mobility, or AAM. The vision of AAM 

is that of a safe, automated, and affordable air transportation 

system for passengers and cargo in both urban and rural 

locations.

Compared to commercial airliners, the aircraft that fly in this 

new airspace are small. Many of these aircraft are Unmanned 

Aerial Vehicles, or UAVs, meaning they are self-flying or 

autonomous. Because of their size, UAVs can be greatly 

affected by weather conditions. Precipitation can impact the 

effectiveness of the propellers used to power them. They can 

also be adversely affected by cold weather; onboard batteries 

that power UAVs become less efficient in colder temperatures. 

As a result, the UAV’s flight time decreases as it gets colder.

If there is more than a light wind, the speed of a UAV will be 

affected by the push of the wind. The wind sometimes blows 

from directly behind the UAV; this is known as a tailwind and 

it increases the speed of the UAV without changing its flight direction. In contrast, when the wind blows from directly in 

front of the UAV, this is known as a headwind. This slows the UAV down without changing its flight direction.

If the wind blows from a direction perpendicular to the UAV’s motion, it is known as a crosswind. The UAV moves 

through the air at a certain speed called the airspeed. With a crosswind, the air moves at a constant speed, called the 

wind speed, in a direction perpendicular to the airspeed. The main effect of the crosswind is to push the flightpath in 

the direction of the wind. The airspeed combined with the wind speed is known as the groundspeed. The groundspeed 

describes the actual movement of the UAV.

Figure 2. When there is a crosswind, the airspeed and wind speed combine to determine the groundspeed.

Figure1. https://pixabay.com/photos/palm-treeswind-windy-weather-4293013/ (Note: Image altered 

to include drone. Credit: Pixabay/NASA)
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 4 (PYTHAGOREAN THEOREM) STUDENT GUIDE | 3 

CALCULATING SPEED WITH HEADWINDS OR TAILWINDS

Tailwinds blow from behind the UAV. To calculate the groundspeed, the airspeed and the tailwind are added together. 

Headwinds blow from in front of the UAV, so the groundspeed is calculated by subtracting the headwind from the 

airspeed.

groundspeed = airspeed + tailwind OR groundspeed = airspeed − headwind

USING THE PYTHAGOREAN THEOREM WITH CROSSWINDS

According to the Pythagorean Theorem, if two sides of a right triangle are known, the other side can be calculated. 

Mathematically, it’s expressed as:

Sides (a) and (b) are the shorter sides of the triangle and meet at a 90 degree angle, while (c) is the hypotenuse.

In this activity, sides (a) and (b) will represent the wind speed and the airspeed. Because of the commutative law, 

it doesn’t matter whether side (a) or side (b) represents the airspeed or the wind speed. Side (c) represents the 

groundspeed.

Example: A small drone flies north with a speed of 15 and there is a crosswind from the east that has a speed of 

5 . What is the groundspeed of the drone?
4 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 4 (PYTHAGOREAN THEOREM) STUDENT GUIDE

PART 1: SOLVING FOR GROUNDSPEED

A company uses package delivery drones to deliver its products to customers. These drones fly with an airspeed of 

60 when carrying a package and 80 when not carrying a package.

1. A drone is carrying a package to be delivered to a customer. As it flies, it encounters a headwind of 8 . Calculate 

the groundspeed for the drone.

2. After dropping off the package, the drone flies back in the opposite direction. Now it is not carrying a package and 

the wind is blowing from directly behind it. Calculate the groundspeed for the drone.

3. If the drone carries a package and encounters a crosswind of 9 , what is the groundspeed?

STUDENT ACTIVITY
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 4 (PYTHAGOREAN THEOREM) STUDENT GUIDE | 5 

4. Complete the following chart:

5. An air taxi is trying to fly to a spot that is directly east of the vertiport from which it takes off. There is a wind blowing 

from the north toward the south. When programming the drone’s flightpath (the airspeed and its direction), which of 

the three paths shown below (A, B, or C) should the programmers use? Explain why you chose the answer you did.

Airspeed Wind Type and Speed Groundspeed

30 Headwind of 7

75 Crosswind of 12

50 Crosswind of 15

45 Tailwind of 5

90 Crosswind of 9

40 Crosswind of 12

Figure 3. The three possible paths for the drone’s flight. Credit: USGS
6 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 4 (PYTHAGOREAN THEOREM) STUDENT GUIDE

PART 2: SOLVING FOR AIRSPEED OR WIND SPEED

1. An engineer looks at the data from an air taxi and notices that it achieves a groundspeed of 53 when flying 

northward through a headwind, and 68 when it is flying southward. What is the airspeed of the taxi? Show your 

work.

2. What is the wind speed in question 1? Show your work.

3. Another air taxi has an airspeed of 50 , but it is flying with a crosswind. The pilot measures the air taxi’s 

groundspeed at 50.8 . Use the Pythagorean Theorem to calculate the wind speed.
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 4 (PYTHAGOREAN THEOREM) STUDENT GUIDE | 7 

4. Complete the following chart:

Airspeed Crosswind Speed Groundspeed

15 25.00

5 40.31

35 36.40

45 46.84

4 18.44
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