STEM LEARNING:

Advanced Air Mobility: Flight 

Control Math 3 (Distance/Speed)

Student Guide

www.nasa.gov

National Aeronautics and Space Administration
2 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 3 (USING THE DISTANCE AND SPEED FORMULAS–STUDENT GUDIE)

AIR METRO

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 settings.

One aspect of AAM, called air metro, is quite similar to 

public transportation systems found in many communities 

around the country. Air metro vehicles carry small groups 

of passengers along prescheduled routes. In most cases, 

these electrically powered vehicles are autonomous, 

meaning that they are controlled by 

a computer.

Air metro vehicles can only takeoff and land from certain 

facilities called vertiports. Vertiports can be standalone 

buildings, or terminals placed atop exiting buildings. To 

maximize the convenience of air metro, vertiports are in both downtown and suburban areas.

DISTANCE FORMULA

Distance formula can be used to determine the distance between two points on a graph.

Distance between two points: P1 (x1, y1) and P2 (x2, y2)

Example: Determine the distance between a point at (5, 6) and a point at (26, 14) where each point on the graph 

represents 1 kilometer.

Figure 1. Air metro carries small groups of passengers between 

vertiports following prescheduled routes. Credit: NASA
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 3 (USING THE DISTANCE AND SPEED FORMULAS-STUDENT GUIDE) | 3 

SPEED FORMULA

The speed formula is used to determine the distance an object moves in a certain amount of time. To calculate the 

speed, divide the distance by the time.

Example: A package delivery drone flies 22.5 km in 15 minutes. What speed is the drone flying? 

By mathematically rearranging the formula, you can determine the formulas for calculating distance or time. 

 

STUDENT ACTIVITY

Engineers have designed and built an air metro system in Indianapolis, Indiana. Initially, the system has three 

downtown vertiports and seven vertiports scattered throughout the suburbs (figure 2). As shown in figure 3, the system 

has four loops that the aircraft follow.

Using the distance and speed formulas, you must help develop the schedule for the air metro vehicles.

Important: 

• All distances should be in kilometers (km) and all times should be in minutes (min).

• All speeds should be in kilometers per minute (km/min).

• Each square of the graph is equal to 1 km.

***OR***
4 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 3 (USING THE DISTANCE AND SPEED FORMULAS–STUDENT GUDIE)

The coordinates for the vertiports are given in the following table:

Vertiport Number Coordinate (x) Coordinate (y)

1 0 0

2 1 4

3 3 2

4 -11 7

5 -11 13

6 -8 -3

7 1 15

8 12 12

9 13 -2

10 20 6

PART 1 : USING THE DISTANCE FORMULA

Begin by determining the distances between the various vertiports. Remember that each square is equal to 1 km. Use 

the distance formula to fill in the missing information in the data tables:

Blue Loop

Distance (km)

Distance between vertiports 1 and 6 8.5

Distance between vertiports 6 and 4 10.4

Distance between vertiports 4 and 5 6.0

Distance between vertiports 5 and 1 17.0

Purple Loop

Distance (km)

Distance between vertiports 3 and 8 13.5

Distance between vertiports 8 and 10 10.0

Distance between vertiports 10 and 9

Distance between vertiports 9 and 3
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 3 (USING THE DISTANCE AND SPEED FORMULAS-STUDENT GUIDE) | 5 

Red Loop

Distance (km)

Distance between vertiports 2 and 5

Distance between vertiports 5 and 7

Distance between vertiports 7 and 8

Distance between vertiports 8 and 2

Green Loop

Distance (km)

Distance between vertiports 1 and 2

Distance between vertiports 2 and 3

Distance between vertiports 3 and 1

PART 2: USING THE SPEED FORMULA

1. 1. To determine the speed the aircraft can fly for the suburban routes, a test was performed. In this test, the aircraft 

flew 127 3⁄4 km in 1 hour and 4 min. 

Calculate the speed (show your work):

Speed = ____________________________________ 

2. Using the speed you calculated, calculate the time it takes to fly each leg of the Blue Loop. Show your work.

a. From vertiport 1 and vertiport 6:

___________ minutes
6 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 3 (USING THE DISTANCE AND SPEED FORMULAS–STUDENT GUDIE)

b. From vertiport 6 to vertiport 4:

___________ minutes

c. From vertiport 4 to vertiport 5:

___________ minutes

d. From vertiport 5 to vertiport 1:

___________ minutes

3. Houses continue to be built in the eastern suburb, so a new stop is being considered for the Purple Loop. The 

systems engineers are trying to determine a good location for a new stop.

a. The desired flight time to the new stop is between 2.5 min and 8 min. Using the speed you calculated previously, 

calculate how close and how far the new stop can be.
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 3 (USING THE DISTANCE AND SPEED FORMULAS-STUDENT GUIDE) | 7 

b. The engineers have narrowed the search down to two possible spots, (14,10) and (17, 12). Determine which one, 

or both, of these would be in the desired distance range from both vertiports 8 and 10.

4. The first schedule below was created for the Red Loop. Unfortunately, there is an error in the portion of the chart 

that contains the times. Assume that the aircraft must be on the ground at the vertiport for at least 1 minute, but no 

more than 2 minutes, making the departures time always 2 minutes later than the arrival time.

Find the error, correct it (as well as any other times that would change), and enter the correct times in the blank 

schedule.

 Enter the correct times in the table above.
8 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 3 (USING THE DISTANCE AND SPEED FORMULAS–STUDENT GUDIE)

5. For the Green Loop, aircraft fly in the downtown portion of the city. To lower the noise and ensure safety, they fly 

slower than their capacity. To calculate the average speed, a researcher collects the following data.

Calculate the average speed, in , of the aircraft. Only count the time spent flying, not the time on the ground. 

Show your work. (Hint: To calculate the total time spent flying, subtract the sum of the times on the ground in each 

vertiport from the time between arriving in vertiport 1 the first time and arriving there the second time.)
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 3 (USING THE DISTANCE AND SPEED FORMULAS-STUDENT GUIDE) | 9 

Figure 2. Locations of vertiports.

Figure 3. Aircraft loops for Indianapolis Air Metro System. 
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