If your drone doesn’t have a GPS unit, how can you figure out how high you’re flying?
The Challenge: Design and perform one or more experiments to help you identify a way to estimate your drone's height. Use your experience to judge which method provides the most accurate estimates.
Think it Through
Before you start, think of some ideas of your own about how to measure the height of a flying drone.
Measuring a horizontal distance along the ground is much easier than estimating large vertical distances or heights. Did you know that if you measure the horizontal distance to an object and the angle at which it appears from that distance, you can calculate its height?
Create a data table (like the one below) to record your measurements and results of calculations... or print this page and use the data table on your printout.
| ||Distance from Pilot to Observer (D)||Observed angle to drone (a)||Observed angle to the location directly below the drone (b)||Drone height (H)|
|Example||30 feet||43°||10°||33.3 feet|
|Trial 1|| || || || |
|Trial 2|| || || || |
|Trial 3|| || || || |
Think it through: Questions to consider
Before collecting data, discuss the following questions with your group:
- How many trials will it take for you to feel confident your final answer is accurate?
- How might you check if your answer is reasonable?
Fly and Collect Data
Set up a flight zone so the drone pilot and observer are a known distance apart. For instance, you might stand on a sports field so you are 10 yards (30 feet) apart.
Pilot: Fly the drone straight up and hover directly overhead at the height you want to measure.
Observer: Use a level app on a smartphone (or make and use a simple inclinometer) to:
- Measure and record the angle to the drone - you will use this value to calculate the height of the drone above eye level.
- Measure and record the angle to the spot directly below the drone - you will use this value to calculate the height of your eyes above the ground.
- Use the angles and formulas (which use the tangent function - tan - on a scientific calculator) to calculate the height of the drone above the ground.
Use the two angle measurements together to calculate the height of the drone. As shown in the diagram below, the height (H) of the drone equals the height above eye level (A) of the drone plus the distance below eye level (B) of the location directly beneath the drone.
Use the horizontal distance to the drone (D) along with the tangent function ("tan" on a scientific calculator) to calculate the distance A from angle ∠a. Use the horizontal distance (D), tangent function, and angle ∠b to calculate distance B.
Here is a sample calculation using the values in the Example row in the table above of D = 30 feet, ∠a = 43° and ∠b = 10°:
A = D x tan ∠a = (30 feet) x tan 43° = (30 feet) x 0.93 = 28 feet
B = D x tan ∠b = (30 feet) x tan 10° = (30 feet) x 0.18 = 5.3 feet
H = A + B = 28 feet + 5.3 feet = 33.3 feet
After you fly and calculate the drone's height, discuss:
- What can you do with the information about the height of your drone?
- How else might you use the technique you used to estimate height?
- What other objects might you use this technique to measure?