# UAS & Newton’s 2nd Law

## Finding the Horsepower of the Parrot Mambo Drones using the concept of Force=Mass x Acceleration.

**Disclaimer: This is Physics so I am going to get a little technical; however, we are simplifying some. Here are a few of the formulas we are working with.*

**F=MA Power=W/T Work=FD Horsepower=750 watts Nm=J**

To find the Horsepower of the Mambo Drones first the students need to find their Hp to understand the process. How does one fine their Hp? Well, Stephen Lynch RSC Physics Lab Technician developed an excellent experiment.

Start with a flight of stairs. The height of the stairs is 1.77m, but I am getting ahead of myself. The student starts at the bottom of the stairs while their lab partner is at the top of the stairs. The student at the top of the stairs is equipped with a stopwatch. The goal of this is to collect a set of data points and determine an average time it takes the student to ascend the flight of stairs. When the student’s foot touches the bottom step, their partner will start the stopwatch. When the student’s foot touches the top step, the stopwatch will stop. They will then collect 4-5 sets of this data and average the time in seconds. The session I participated in the average time was 2.235s.

We must also have the weight of the individual running up the stairs. Let us put the weight of the student at 220lbs. We do have to change those pounds to kilograms so we can then convert the kilograms to Newtons. All right, 220lbs. converts to 100kg.

We know the acceleration of Gravity is 9.81 m/s2, right? Well, we have to convert the weight further into Newtons, like I said earlier, because F=MA. All right, we have our weight in kg, multiplied by 9.81 m/s2 (Gravity) which equals our weight to 981N. Now that we have our weight, we need to find how much Work we put into going up the stairs.

So Work=force x distance. Work=FD, remember when I was trying to get ahead of myself earlier, we come full circle now. Ok, we take the 981N (the weight we just converted) and multiply it by 1.77m (height of the stairs) which equals 1736.37J. J=Joules. Work is represented in Joules.

What is Power? Power is Work over Time; this in turn will give you Watts. Let us take 1736.37J and divide by the average time up the stairs 2.235s. This equals 776.9watts. Now, did you know Horsepower=750 watts? Take 776.9watts and divide it by 750watts. This gives you 1.04hp. Our data has now concluded a person with the weight of 220lbs. utilizes 1.04hp to run up one flight of stairs.

Now that we understand F=MA and that we can determine the Hp from the Work (and how to do the conversions); we can now figure out the Hp of the Mambo Drones. Below is a picture to show you how we collected the data sets of time and distance.

Start by finding the Mass of the Drone. The Mambos are approx. 0.0675kg. Multiply by Gravity (9.81m/s2)=0.662N. Take your average height from your data set you ran.

You might ask me, how do I get the set of data points of height and time? To get the average height and time for the Mambos as they are ascending; take a meter stick, stopwatch, and Mambo, hold the meter stick upright. Set the Mambo on the floor. Here you will launch the Mambo and time the distance it rises until the Mambo levels (measurement is to be taken at the feet of the Mambo).

How fast does the Mambo accelerate? Take the average time you collected each time the Mambo leveled out after launch, we got 0.97s at a distance of 0.63m. Ok, now remember we have to convert the weight from Newtons to Joules, so take 0.662N x 0.63m=0.417J. To find the Power take the 0.417J and divide by the time 0.97s because Power=Work over Time. This calculates to 0.405watts. Hp=750watts, so we convert 0.405watts/750watts=0.0054hp.

The student’s conclusions with the Mambo Drones is they averaged approx. 0.0009hp on most of the Mambos. After these findings, they started adding different weight to the Mambos and repeating the process.

*Article last updated December 2019*

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