Understanding Model Rocket Stability

Model rockets are stable when they move under power in the direction that they are initially pointed. Similar to an arrow, a model rocket has fins on a long body. The fins add a large surface area to the rear of a model rocket that increases the air resistance and moves the center of this resistance towards the rear of the rocket. The center of all the resisting forces on a model rocket is called the center of pressure.

A model rocket or any object moving through the air will rotate around its axis at the center of the weight distribution. This is called the center of gravity. This is where the rocket balances horizontal to  the ground when you hold it loosley by the tips of two of your fingers. On a model rocket, the center of pressure (CP) needs to be behind the center of gravity (CG) for the rocket to be stable.

As a rocket is pushed through the air, the center of air resistance (CP), rotates behind the center of rotation (CG), causing the rocket to point forward. Because of this action, the rocket is pointed into the relative wind during flight.

Generally, the distance the CG should be ahead of the CP is equal to 1 or 2 times the diameter of the body of the rocket. Being closer than this could cause the rocket to wobble or even try to reverse its direction by looping in flight. Being farther than this could cause the rocket to be overly stable and veer off into a moderate wind instead of going straight up. This behavior is called “weather-vaning.” Of the two options, over stability is more desirable.

Finding the CG on a rocket, large or small, is relatively easy. Finding the CP is more difficult. One of the easiest methods for determining the stability of model rocket is to tie a loop of string around the CG of a model rocket and swing it around your head to see if the rocket is stable. This is called the “Swing Test”. This method works on smaller rockets, but does not necessarily prove that a larger rocket is stable or unstable. This is due to practical limits on the length of a string you might be able to swing around your head.

For example:

Example 1: At 10 feet of string length, a 24 inch rocket has the nose and tail moving through the relative wind at an angle of 2.9 degrees from ideal, or a total difference between the nose and the tail of 5.8 degrees. A rocket of this length will probably be able to be tested at this length.

Example 2: At 10 feet of string length, a 48 inch rocket has the nose and tail moving through the relative wind at an angle of 5.8 degrees from ideal, or a total difference between the nose and the tail of 11.6 degrees. A rocket of this length has too much angular distance between the nose and the tail relative to the forward motion in the wind and probably would not be able to be tested at this string length.

Large or heavy rockets are difficult to swing and could be damaged if the rocket hits a stationery object or person during the test. A better way of determining the stability of rocket is to determine the CP by calculation. One of the best known methods is called the Barrowman method.

Barrowman Method of Predicting Stability

The Barrowman method calculates all the individual pressure changes along the rocket from nose to tip. After each change is calculated, the total of each element is added and a ratio is calculated from the same elements multiplied by the force value for each element.

To use the equations, the values measured from the rocket as illustrated above are substituted into the equation. Refer to the definitions below while taking measurements:

LN = Length of Nose d = Diam. of Base Nose
dF = Diam. of Transition Front
dR = Diam. of Rear Transition
dT = Diam. of Rear Transition
XP = Distance to Transition
CR = Fin Root Chord
CT = Fin Tip Chord
S = Fin Span
LF = Fin Mid-chord Line
R = Radius Body at End
XR = Fin Sweep
XB = Distance Nose to Fin
N = Number of Fins

Barrowman Calculations
While this task seems daunting it can be done in stages using a calculator with square root capability. If you don't want to go to this trouble, you can download a free Winroc windows based software program the from our website at ModelRockets.us that can do this for you.

The following terms are substituted for general math symbols:
* = Multiplication Function
/ = Division Function
^ = Square Function
Sqr = Square Root Function

Barrowman Basic Equation
CP = (CNN * XN + CNT * XT + CNF * XF) / (CNN + CNT + CNF)

Here the CP value represents the center of pressure. Use the following  factors and calculations and then plug the numbers in the  Barrowman Basic Equation above (repeated at the end of this blog).

Calculating the Nosecone Values
All Shapes of Nose Cones: CNN = 2
For Conical Nose Cones: XN = 0.666 * LN
For Ogive Nose Cones: XN = 0.466 * LN
For Parabolic Nose Cones: XN = 0.5 * LN
For Hack Nose Cones: XN = 0.5 * LN
For Von Karmen Nose Cones: XN = 0.563 * LN

Calculating the Transition Values (if there are any)
CNT = 2 * (((dR / d) ^ 2) - ((dF / d) ^ 2))
XT = XP + ((LT / 3) * (1 + ((1 - (dF / dR)) / (1 - (dF /dR) ^ 2))))

Calculating Fin Values
The LF value is needed for trapezoidal fins only. It can be measured or calculated with the following equation:

LF = Sqr (S ^ 2 + (XR + (CT / 2) - (CR / 2)) ^ 2)

Trapezoidal Fins
FT1 = 1 + (R / (S + R))
FT2 = 1 + Sqr(1 + ((2 * LF) / (CR + CT)) ^ 2)
CNF = FT1 * (((N * 4) * (S / d) ^ 2) / FT2)

FT3 = CR + CT
FT4 = (FT3 - ((CR * CT) / FT3)) / 6
XF = XB + ((XR / 3) * ((FT3 + CT) / FT3)) + FT4

Elliptical Fins
FT5 = (4 * N * (S / d) ^ 2) / (1 + Sqr(1 + (1.623 * (S / CR ) ^ 2)))
CNF = FT5 * (1 + R / (S + R))

XF = XB + 0.288 * CR

Final Results
After calculating each element of the rocket. They are applied in the final equation:

CP  = (CNN * XN + CNT * XT + CNF * XF) / (CNN + CNT + CNF)

Use the CP value measured from the tip of the nose cone of your rocket. This location is the center of pressure of your rocket. If your rockets CG is 1or 2 tube diameters ahead of the CP then most cases your rocket will be stable and you are ready to go.

Note:
There is an exception to the CP to CG distance rule that applies to short fat rockets. These kind of designs can often fly very well with a CP to CG distance of 1/2 to 1 tube diameter.

For more information go to ModelRockets.us

What’s Important for Model Rocket Performance

I get many questions from beginning model rocket modelers that want to know how to design model rockets for the best altitude performance. This interest varies between those who just want to get the best performance from a custom designed rocket to those who are involved in Science Fair or school projects. Most often the focus of the questions are on design issues associated with aerodynamic shape such as the nose cone or fin shape and often the questions center on just length and diameter. In the following discussion, I'll try to unravel the issues about model rocket performance.

So What's Important?

To help divide the areas involved in model rocket performance, I've listed most of the factors that affect flight performance.

Gravity - A big factor. The only way to reduce gravity is to launch a rocket at an angle not perpendicular to the ground. Launching at an angle will increase the distance a rocket travels before coming back down. However, a rocket will not reach its highest altitude unless it is launched straight up, perpendicular to the ground. I’ve brought the issue of gravity up to illustrate that the most important issue regarding model rocket performance is:

Weight - As you can't change gravity, you can get the same affect by reducing the weight. This is because the speed of the rocket at engine burnout is proportional to the weight of the rocket. The following simplified equation illustrates this:

v = (I * g)/W

Where as:
v = Max Velocity in Feet per Second
I = Total Motor Impulse in Pound Seconds
g = Gravity at 32.2 Feet per Second Squared
W = Weight of Rocket at Burnout in Pounds

In this equation gravity is a fixed constant. So only changing motor impulse or changing the weight of the rocket will affect the burnout velocity of the rocket.

To use this equation you can convert the typical motor impulse ratings of newton-seconds to pounds by dividing newton-seconds by 4.448. You can also convert typical rocket weight in ounces to pounds by dividing ounces by 16.

Power - Increasing the power has the same affect as reducing the weight. For instance let’s apply the velocity formula to the following examples...

Rocket with an impulse of 5 newton-seconds equals 1.124 pound- seconds and 10 newton seconds at 2,248 pound seconds. Weight of 4oz equals .25 pounds.

Applying the formula v = (I * g)/W yields:

Change the weight to .125 Pounds hass a result ofg
(1.124 * 32.2) /.125 = 289.54 feet per second

Change the impulse to 2.248 pound seconds changes the result to:
(2.248 * 32.2) /.25 = 289.54 feet per second

As you can see, doubling the total impulse or cutting the weight in half has the same affect of doubling the velocity.

The above burnout velocity calculations do not take in to account the effect that aerodynamic drag has on the velocity. In the following section we will begin to deal with this issue.

Aerodynamic Drag

Aerodynamic drag can have a significant impact on the velocity of a rocket in flight. For instance, the calculation of drag force is:

D = 0.5 * p * (V^2) * Cd * ((r ^ 2) * 3.14159)

 

Where as:

D = Drag

p = Air density in kg/m3

v = Max velocity in feet per second
Cd = Drag coefficient
r = Diameter of rocket divided by 2

The velocity has the greatest affect on drag in this calculation since it is squared. However, as the earlier equation for velocity is calculated separately, we will consider this to be a constant in this calculation.

Air Density - Air density is about .97 at sea level and 70F. There is little that you can do about it other than launch on a hot day or take a trip up to the mountains where the air is less dense to launch.

Drag Coefficient - The drag coefficient is usually less than 1. Most rockets fall between .5 and .75. Only a very bad design would exceed 1. We will discuss this in some detail in the following section.

Diameter of the Rocket - In the above calculation, the diameter is divided in two, then the result is squared and multiplied by 3.14159 or PI. This calculation will give you the area the rocket faces into the wind or how much the air is displaced. Independent of the velocity value, the diameter of the rocket is the single largest factor in drag force calculations. The drag nearly quadruples as the rocket diameter only doubles.

Aerodynamic Shape - The single factor which describes the shape of model rocket and the finish is the drag coefficient. Take a look at the 2 rocket designs on the right. The one on the left looks considerably sleeker than the one on the right.

Based on a rocket with a good finish, the design on the left would come in with a .5 Cd (drag coefficient) while the one on the right would come in with a slightly higher Cd value.

So What Does All This Mean?

Aerodynamic shape has an impact on the drag force the rocket sees in flight. However, the diameter of the rocket has a larger  impact on drag calculations.

It is understood that the height the rocket is able to obtain is based on velocity over time. The import factors in the velocity are the weight and power of the rocket.

To achieve better performance from a rocket and higher altitude flights, focus on weight and power, first, then rocket diameter and lastly aerodynamic shape.

For more information go to ModelRockets.us