# GoFly

### The AJ-1

The AJ-1 was going to be my entry into the HeroX **GoFly **competition. The competition was to design (and eventually build) a single seater vehicle capable of safely and quietly carrying one person a distance of 20 miles. The biggest catch was that the vehicle had to be completely contained within an 8.5 ft sphere. So the distance between any two points could not be greater than 8.5 ft.

This made it difficult because lift is largely determined by the surface area of lifting surfaces. For a vehicle with rotors, the area in question is the area swept out by the rotors. The largest a blade can be for this competition is then 4.25 ft which is very restricting on what it can do for lift.

Anyway, I wound up not entering the competition because I did not finish my design on time. I did, however, do quite a bit of work and would like to revisit this in the future, especially without the restrictions of the competition.

### Human Sized Quad Copter

I've always kind of wondered why we haven't seen a human sized quad copter yet. Turns out there are a few people doing it and one of them is called **Kitty Hawk** (wonder why). They update their site regularly and have gone through at least a few public iterations of their design. Also, it's not quite a quad copter. One design had 6 blades and the current one looks to have 8. But in any case, it was possible.

In any case, in order to meet the original size requirements by the GoFly competition, I decided to go with a human sized quad copter.

Here was my proposal for the design.

I previously was a member of my universities SAE team where we designed a formula car every year so I took a lot of inspiration from that - the tube steel frame, racing seat, roll cage, etc. I figured that if I could place each component so that it fit within the build envelope, I could figure out the details of each later - namely, what motors I would use, which blades I would use, and how to calculate the power requirements for the batteries.

### Power Source

I started off the design of AJ-1 by selecting what type of fuel to use as a power source. Per the GoFly rules, the flying machine had to use power sources that were available to the general public and could be easily understood. Iquickly decided to use electricity because of its wide availability, cleanliness, and resourcefulness. Furthermore, electric motors generally make less noise than a fuel burning engine and since noise is a gradable metric in this competition, it was the logical choice to go with.

This would mean I would be designing the AJ-1 to use electric motors and there are two type of motors to choose from, AC or DC. While DC motors are a little simpler as they don’t require inverters to power them, AC motors tend to be better for high performance applications {source}. They require less maintenance and the dollar per horsepower is slightly better. This combined with the commercial availability of AC motors suited to this application aided me in deciding to go with an AC motor power source.

### Blade Form Factor

With the power system in mind, I had to decide on the blade layout for the AJ-1. As mentioned before, the GoFly rules require that the entire aircraft fit inside an 8’ 6” sphere. If I went the route of the traditional helicopter with one blade, then I would also need some sort of tail boom to counteract the main rotor torque. Because of this size requirement, I really didn’t have room for this. So I next considered a multi-rotor system.

An important variable in calculating how much lift a rotorcraft can produce is determined by the surface area swept out by its lifting rotors. In order to optimize this swept-out surface area, I would want the blades to occupy as much area as possible inside of the 8’ 6” sphere. Therefore I would need to place the blades at the cross-section at the center of the sphere. In order to account for machining tolerances and just to have a small margin of safety, I decided to design around a slightly smaller sphere with a diameter of 8’ 5”. Since being too large would immediately eliminate our chance at competing in the competition, I decided that this one inch was a worthy price to pay.

Using blades of equal size, I came up with the following chart to determine how much surface area N number of blades would occupy inside of an 8’ 5” circle.

While it can be seen that 6 blades (5339 in^2) produces the most surface area, 4 blades is a close second with 5281 in^2. The weight of two added motors would easily negate these small gains in surface area so four blades seemed like the optimal solution.

I did still consider a co-axial rotor system but after doing some research, I wanted to avoid the complex machinery required to make that work. One of the personal goals I set for this competition was to be able to make as many parts as possible on either a 3-axis mill or a lathe. I didn’t want any part of the AJ-1 to require rare or expensive tools to construct.

Therefore I decided on the quad copter arrangement. Quad copters are already known for their maneuverability, speed, and ability to be easily operated [source]. They can easily perform all yaw, pitch, and roll maneuvers of a typical aircraft and are reliable.

### Blade Element Theory

William Froude was a hydrodynamicist and engineer that developed blade element theory. While he originally developed it to predict the performance of marine propellers, it proved equally valuable in determining blade characteristics for flight. The process involves mathematically breaking a single blade into several cross sections over the length of the blade and analyzing the forces acting on each one. The forces can then be summed up in order to determine performance characteristics of the blade.

The equation for Thrust from Blade Element Theory is

ΔT = .5 · ρ · V² · c · B · CL · dr

where

ΔT = thrust (lb)

ρ = air density (lb/ft^3)

V = velocity (ft/s)

c = chord length (ft)

B = number of blades

CL = Coefficient of Lift

dr = distance from center (ft)

**Thrust (T)** - In order to assure that the AJ-1 can accelerate vertically, I will assume that a thrust 10% greater than the weight of the vehicle will be sufficient. This comes out to 940 pounds. Therefore the summation of slices from Blade Element Theory must equal a thrust of 940 pounds or greater for the AJ-1 to have enough power to complete the GoFly course.

**Air Density (ρ)** – Since at this point, the location of the event has not been disclosed, we will use an assumed height of 2000 feet. This is the average height of land in the U.S., 1750 feet (source), plus 250 feet flying altitude to bring us to a round 2000. The air density at this altitude is 0.063 lb/ft^3 (source).

**Velocity (V)** – This is the linear speed that the blade section is moving at. We want to minimize this as blade speed has a direct effect on motor RPM and therefore noise generated. Since a large part of the competition is creating a quiet vehicle, we want to keep the RPM’s as low as possible in order to sustain flight. We must optimize the other variables to take this into account.

**Chord Length (c)** – The chord length is the distance from the leading edge of the blade to the trailing edge. Selecting a chord length will be largely based on availability of parts since we would rather buy blades off-the-shelf than fabricate them. We will use a 4” chord length as an estimate.

**Number of Blades (B)** – We have decided to use 2 blades per rotor. As long as this will give us the thrust we need, a low number of blades will reduce aerodynamic drag on the motor and therefore require less horsepower. ***[Some book said one blade would be ideal if it could be balanced. Find this and quote it.]

**Coefficient of Lift (CL)** - NACA 4-digit airfoils are well documented for aerodynamic characteristics so at this portion of the design phase, I used a 4-digit airfoil for calculations and left higher dimension airfoils for later optimization. I have decided on a NACA 2412 airfoil due to its CL and CD characteristics and relatively wide availability. At an angle of attack of 7 degrees, a NACA 2412 airfoil as a coefficient of lift of about 1.00 (source).

**Distance from center (dr)** – This is the distance from the center of rotation to the slice of the airfoil being analyzed. Due to the size constraints, the maximum dr value will be 20.5”. I will also negate values between 0 and 2.5” as this surface will not be generating lift.

Here are our variables as just defined in an easier to read form.

T= 940 lbs

ρ = 0.063 lb/ft^3

V = 2 * p * RPM * dr / 60 (to minimize)

C = 0.333 ft

B = 2

CL = 1.00

Dr = range of 2.5” to 20.5”

Upon calculating the formula with these variables, I determined that a motor RPM of 3500 RPM would work in producing enough lift to maneuver throughout the GoFly course. This is well within the range of most high performance AC motors which is the next component to refine. Next I determined how much motor power would be required to lift the AJ-1 with Momentum Theory.

**Momentum Theory**

To find the power required by the motors, I must determine the induced velocity from the rotors. The equation has been well studied According to Principles of Helicopter Aerodynamics, J. Gordan Leishman p63,

Vi = sqrt(T / (2ρA))

Where Vi is the velocity induced by the rotor and A is the surface area of the rotor. The AJ-1 uses a rotor area of 7.07 ft^2 per motor, or 28.27 ft^2 for all four rotors. This equates to an induced velocity of 16.02 ft/s. This is the first step in determining the power required to produce the thrust required for flight.

There are two types of power; induced power and profile power.

Induced Power (Pi) – the major part of the power induced by the motor that creates lift. Pi = T * Vi.

Profile Power (Po) – The power required by the motor to overcome friction and aerodynamic forces. This is determined by the efficiency of the rotor and

These are tied together with the Figure of Merit (M) – the ratio between the induced power and the total power. It is determined with the following equation.

Po = (Pi – Pi * M) / M

Ptotal = Pi + Po

Using a figure of merit of 0.8, we get an induced power of 157.5 hp and a profile power of 39.4 hp. This leads to a total required power of 196.9. This has to be distributed into 4 motors so each motor must have a power of at least 49.3 hp.

**Motors**

As mentioned earlier, I have decided to use AC induction motors for the AJ-1. Upon doing some research, I came up with the following table of potential candidates to use for all four motors.

After reviewing many different motors, the best choice to go with seemed to be the one with the lowest pound-horsepower ratio, in this case, the AC-15 from EV West. This motor would be able to spin above my minimum required RPM as well as produce the power needed to lift the AJ-1. However I wanted to consider the other ones to see of the power tradeoff would be worth it or if the lower amperage for the AC-23 could lighten the load of the batteries.

The batteries I was considering were rechargeable lithium-ion batteries, specifically, the 18650 and 21700 form factors. These particular batteries have a great energy density as well as the ability to be discharged and recharged hundreds of times. I came up with the following table to decide on batteries to use.

As can be seen in this table, the 18650 in the top row has the greatest energy density and is most likely the best choice. However, the 18650 in row two has a higher discharge rate and the 21700 battery has a greater mAh capacity. These traits could pay off by requiring a lesser number of batteries and lead to a more ideal total weight.

The next step was to determine exactly which battery-motor combination to use. I set the goal of a flight time of 30 minutes. This should be sufficient to make it through the course with energy still left in the batteries. Since points will be awarded for having excess energy capacity after completion of the course, it is beneficial to overestimate total battery capacity.

After comparing the three types of batteries against the AC-15 motor, I came up with the following table.

While the 21700 batteries did have a high energy density, the top-row 18650’s came out on top. This would require 2418 batteries and while it is a lot of batteries to include, it will fucking work.

Well, this is as far as I got. I hope to pick this up again someday but that day is not today.