Optimizing Rocket Shape to Maximize Altitude

By Alexander “Beandip” Calvert

NAR 77390 / A Division / March 2005

This is me and the four rockets I used for my project.

In case you can’t tell, that thing on my head is a drinking hat.

Optimizing Rocket Shape to Maximize Altitude

Objective

For my NARAM R&D project, I built four model rockets with the same weight and internal volume. I put an altimeter in the rockets and flew each of them three times. I recorded how high they went. My hypothesis was that the skinny rockets would go higher than the fat rockets because the skinny rockets have less drag. Fat rockets have more frontal area so they have to move more air out of the way. However, extremely skinny rockets tend to collapse or fold or bend while flying. A skinny rocket might also have too much surface drag. You have to try to make a rocket not too fat and not too skinny.

Methods

Rocket design and construction

Rocket Shape / Length1 / Diameter / Internal Volume1 / L/D Ratio2 / Weight
Fat / 13.5” / 2.60” / 71.6 cubic inches / 5.19 / 220 grams
Medium / 33.9” / 1.64” / 71.6 cubic inches / 20.67 / 220 grams
Skinny / 50.0” / 1.35” / 71.6 cubic inches / 37.04 / 220 grams
Super-Skinny / 95.0” / 0.98” / 71.6 cubic inches / 96.94 / 220 grams

1 Length and L/D ratio exclude the nose cone

2 L/D ratio = Length to Diameter ratio (also called aspect ratio)


The four rockets were modified from rockets my dad and I already had. All the rockets were lengthened by adding more tube. We added payload sections for the altimeter. We added clay to adjust the weight of three of the rockets to match the weight of the heaviest rocket (220 grams without motor).
The fins on the four rockets aren’t exactly the same, but they are similar. They all have three or four medium size fins. We did not include the nose cone in the length measurement or volume calculations, but they all had similar shaped (ogive) nose cones.

Altitude measurements

I used a Mini Alt/WD Altimeter, made by PerfectFlite (http://www.perfectflite.com). My dad used one of his large high-power rockets to test the altimeter the first time.

The data from my Dad’s test flight is shown below. His large rocket went over a mile high and about 500 mph. It deployed two different sized parachutes, and stayed in the air for 3 minutes. The altimeter worked well.

Now I was ready to move the altimeter into my rockets.


Motors
I used Estes D12-5s and D12-7 motors for each flight. These motors use black powder as propellant. The “D” means that they have between 10 and 20 Newton-seconds of total impulse, which is the thrusting power of the motor. The Estes D12 has about 17 Newton-seconds of total impulse. The “12” means they have an average thrust of 12 Newtons. If you know the average thrust and the total impulse of a motor, you can calculate the burn time. For this motor, 17/12 =1.42 seconds. The last number is the delay time from motor burnout to parachute ejection. We used 5 and 7 second delays, depending on the rocket. It’s important that ejection happens after apogee, which is the high point of the flight, but not too late. On the first flight of the super-skinny rocket, we used a D12-7 and it almost crashed into the ground!

Launch times and locations

The test flights were made at two different locations in Michigan, Manchester and Three Oaks. The Manchester launch was on January 15, 2005, and hosted by Michigan Team-1 (http://www.team1.org). The Three Oaks launch was on January 29, 2005, and hosted by Tripoli Michiana (http://www.tripolimichiana.org).

Rocket Simulation Software

After completing the flights, we used the RockSim rocket simulation program, made by Apogee Components (http://www.ApogeeRockets.com), to simulate the flights. We graphed the flight simulations and compared them to the actual flights. We ‘backtracked’ the coefficient of drag (CD) for each rocket from the flight data. This means that we adjusted the value of the CD until the simulation altitude was equal to the actual flight altitude.

Budget

Rockets (we already had these) / $0
Components to add length and payload bay / $10
Altimeter (Dad’s) / $0
Rocksim software (Dad’s) / $0
Motors / $40
Gatorade (for my drinking hat) / $5
TOTAL / $55


Results

AB

CD

A. Skinny rocket on launch pad.

B. Skinny rocket igniting.

C. Skinny rocket blasting off.

D. Super-skinny rocket landing.

Two examples of flight profile data, one from each launch. The altimeter automatically detects launch as a sudden drop in pressure equal to 100’ altitude.

Rocket Shape / 1st Flight / 2nd Flight / 3rd Flight / Average
Fat / 345 ft.1(D12-5) / 407 ft. (D12-5) / 329 ft. (D12-5) / 360 ft.
Medium / 491 ft. (D12-5) / 482 ft. (D12-5) / 443 ft. (D12-5) / 472 ft.
Skinny / 386 ft. (D12-7) / 590 ft. (D12-7) / 435 ft. (D12-5) / 470 ft.
Super-Skinny / 327 ft.2(D12-7) / 424 ft. (D12-5) / 425 ft. (D12-5) / 392 ft.

1 The fat rocket landed in a stream on the first flight.

2 The super-skinny rocket ejected late, bent, and had to be repaired with a splint.

The medium rocket went highest (472’), but the skinny rocket went only 2 feet less, on average. The super-skinny rocket came in third (392’), and the fat rocket finished last (360’). As expected, the fat rocket was slowed down most by the effect of aerodynamic drag.

Discussion

A rocket has to overcome two forces: gravity and aerodynamic drag. Aerodynamic drag is the force that resists the movement of the rocket through the air. Drag depends on frontal area, which determines how much air is displaced as the rocket moves through it. Frontal area can be measured directly. In addition, drag is caused by friction between the outside of the rocket and the air. The amount of friction depends on the shape of the rocket and the texture of its surface. The combination of these is called the “coefficient of drag” or “CD”. It’s very difficult to predict the effects of shape and texture on drag without flying a rocket or testing it in a wind tunnel. If you know everything else about the flight of a rocket, including weight, diameter, engine thrust curve, and altitude, you can use a rocket simulation program to calculate the CD. Once you know the CD of a rocket, you can accurately predict the altitude using different engines and payloads.

I started out expecting that the skinny rockets with the least frontal area would go highest. This would be true if all the rockets had the same CD. What I found was that rockets with a normal rocket shape went higher than extra fat or extra skinny rockets. The skinny rockets must have a very high CD! I used RockSim Rocket Simulation Software to simulate the flight of each rocket by modeling the shape of the rocket and plugging in values for the weight, diameter, and engine thrust curve. I adjusted the CD values until the simulated altitude matched the average altitudes from the three flights. This is called “backtracking” to get the CD. Here is what I found:

Rocket Shape / Average Altitude / Calculated CD
Fat / 360 ft. / 0.59
Medium / 472 ft. / 0.51
Skinny / 470 ft. / 0.77
Super-Skinny / 392 ft. / 3.15

Why is the CD for the Super Skinny rocket so high? There are several reasons. The main reason has to do with flow of air down the outside of the rocket. Over short distances, the air flows smoothly along the rocket’s skin. As the distance increases, the flow becomes more and more turbulent due to friction with the skin of the rocket and surface defects. By the time the air flows from the nose to the tail of the super skinny rocket (8 feet), the air flow is choppy and slow. Another reason for high CD is flexing. The super skinny rocket is flexible, and it wobbles and bends some when it flys. This can cause even more drag.

People who design real rockets must already know that extremely tall and skinny rockets are not necessarily more efficient. Looking through the book “Rockets of the World” by Peter Alway, there are not any real rockets that are very skinny. America’s Vanguard and Scout rockets were about as skinny as they get, with L/D ratios of about 20 (same as the Medium rocket in my experiment).

Competitive model rocket flyers also know that very skinny rockets have more drag than normal shaped rockets. There is an event called Super-Roc Altitude (SRA) that multiplies the length of your rocket by the altitude to give you a score. I learned that making your rocket longer will not necessarily give you more points, because the aerodynamic drag will be much higher. I plan to use this information to design a rocket that will win the contest.

RockSim model of the Fat Boy rocket, used in flight simulations.

RockSim simulation of the Fat Boy rocket, with CD adjusted to 0.59 to make simulated altitude the same as the average observed altitude (360’). Acceleration is in green, velocity in yellow, and altitude in blue.


Optimizing Rocket Shape to Maximize Altitude

By Alexander “Beandip” Calvert

NAR 77390 / A Division / March 2005

Summary

For my NARAM R&D project, I built four model rockets with the same weight and internal volume. I put an altimeter in the rockets and flew each of them three times. I recorded how high they went. My hypothesis was that the skinny rockets would go higher than the fat rockets because the skinny rockets have less drag. Fat rockets have more frontal area so they have to move more air out of the way. However, extremely skinny rockets tend to collapse or fold or bend while flying. A skinny rocket might also have too much surface drag. You have to try to make a rocket not too fat and not too skinny.