3. Aerodynamics and its Role in Experimental Rocket Design
Introduction
Those of us who started out in this hobby by building and flying model rockets quickly learned that aerodynamics plays a big role in how high our model rockets would fly. We learned the importance of sanding and painting the rockets to give all the external surfaces as smooth a finish as practical. Fins were carefully rounded at the leading edge and tapered at the aft end. This was done to improve aerodynamic efficiency, or "cleanness". We were rewarded with higher flights that would not be achieved otherwise. As well, aerodynamic cleanness refers to lack of protruberances (e.g. launch lugs) that degrade the flow of air over the rocket, or sharp changes in contour.
It is therefore very interesting that for most EX rockets (and here I am refering to LoPER class EX rockets and to a lesser extent MiPER class rockets), aerodynamic cleanness is notably less important than it is for model rockets. This is mainly due to two reasons
1) Ballistic coefficient
2) Motor choices
Let's examine these two factors.
Ballistic coefficient: Ballistic coefficient is the ability of a moving body to overcome air resistance. The higher the ballistic coefficient, the more slippery the object as it moves through the air. Ballistic Coefficient (BC) is defined as:
where:
m = mass of the rocket
Cd = drag coefficient of rocket
A = cross sectional area of rocket (normal to velocity vector)
Model rockets are lightweight compared to typical EX rockets.
As an example, my Xi EX rocket has a typical empty mass of 2600 grams. The body diameter is 3 inches (76.2mm), giving a cross-sectional area of 4536 mm2. The drag coefficient has been measured as Cd = 0.55 (note that the Xi rocket is not very aerodynamically clean). The ballistic coefficient is therefore BC = 2600/0.55/4536 =1.04 g/mm2. For comparison, I measured the mass and diameter of two model rockets that I have in my collection, the Alpha III and StormChaser. Table 1 shows the BC of these two model rockets in comparison to three of my EX rockets (DS,Zeta & Xi). Also shown, to provide an intuitive feel, is the BC of a golf ball and a ping-pong ball.
Table 1: Ballistic Coefficient Comparison
The two model rockets are twice as slippery when slicing through the air than a golf ball. The three EX rockets are, on average, 5X as slippery as the model rockets. In this sense, more slippery denotes that aerodynamic drag has less influence on impeding the flight of a moving body. Also shown in the table is the ballistic coefficient for the dart vehicle for the SDC Cajun-Dart [1] rocket assembly. The boosted dart concept was used for early sounding rockets used for atmospheric research. The 1.75 inch (45mm) diameter dart , fabricated of steel with lead ballast, served as an inert second stage that capitalized on a very high ballistic coefficient to achieve a great altitude once boosted by a conventional rocket to hypersonic velocity of just over 5000 feet per second (mach 4.5) at an altitude of 7000 feet. The Cajun dart then separated and typically coasted to an apogee of 75 km.
Motor Choices: With model rockets, choice of motor to power the rocket is limited and larger motors are more costly. With EX rockets, there really is no limit on motor choices. Making a motor slightly larger to compensate for a rocket with non-optimum aerodynamic performance generally requires little investment in terms of time, effort or expense. I typically "stretch" my motors to gain additional lifting power. For example, I have done this with the Impulser, stretching it from the initial four grain segments, to five, and then six, for the subsequent Impulser-X and Impulser-XX motors.
Aerodynamic Design Considerations
Understanding the basics of rocket aerodynamics is nevertheless important. Even for LoPER class rockets it is beneficial to know what factors have the greater effect upon aerodynamic performance. Small improvements in aerodynamic design details can provide "free" altitude gains. And it is good practice for designing higher performance HiPER and ViPER class rockets where aerodynamic considerations are very important. Aerodynamic drag is a force which counters the rocket motor thrust force and acts in concert with gravitational force to slow down the rocket. A slower rocket means less altitude gained. At burnout, the rocket has achieved its maximum velocity and likewise maximum kinetic energy (K.E. = mass x velocity2). For EX rockets, this K.E. is converted to Potential Energy at apogee (P.E. = mass x gravity x altitude) less the energy lost (incidentally, in the form of frictional heating) as a result of work done on the rocket by aerodynamic drag force. In equation form, drag force due to air resistance is given by:
[eqn.1]
where
ρ (Greek: rho) = air density (kg/m3 or slugs/ft.3)
V = velocity (m/sec or ft/sec)
CD = drag coefficient of the rocket (dimensionless)
A = frontal area of rocket, where A = ¼ π D2 (m2 or ft.2)
Note that the term ½ ρ V2 is dynamic pressure
Calculating drag force in the transonic/supersonic regime is similar to subsonic, except the dynamic pressure term is different:
[eqn.2]
where
k = gas ratio of specific heats
p = gas (static) pressure (N/m2 or lbf/ft.2)
M = mach number (dimensionless)
The total drag on the rocket is the sum of the drag on the individual components such as nosecone, body and fins, as well as interference drag. The drag coefficient may be represented as such:
CD = CD nose + CD body + CD base + CD fin + CD int + CD lug
CD base is the coefficient for the drag force that results from low pressure at the aft end of the rocket caused by flow separation. CD int is the coefficient for the drag force that results from altered air flow at the location of the fin/body joints. CD lug is the coefficent for the drag force due to the launch lug and its attachment to the body. CD body is typically generated by conical transitions. However, even without transitions, there is a pressure drag correlated to skin friction (boundary layer effect).
Drag force on a rocket is the result of two interactions between the rocket and the surrounding air: imbalance in the air pressure acting on the rocket, and friction of the air sliding past the rocket. For a typical subsonic EX rocket with a length to diameter ratio of 10, frictional drag is dominant. This is clearly seen in the two graphs presented in Figure 1 for a typical subsonic (LoPer class) rocket (shown here ). The graph on the left shows the drag coefficient for the various components that make up the total drag coefficient. The graph on the right breaks down the percentage of total drag for the various drag components
Figure 1: Breakdown of drag for a subsonic rocket
Note that drag is shown as a function of mach number. At low subsonic speeds, the air is essentially incompressible, that is, the density of the air doesn’t change at all as the air changes speed around the vehicle. As a result of this, the drag coefficients are seen to be essentially constant. Above approximately Mach 0.7, however, compressibility effects start to appear, as will be shown later.
As can be seen, nearly one-half the total drag on the rocket is due to body skin friction. Combined with fin skin friction, the total becomes nearly 70% of the total drag. On the other hand, pressure drag due to the nosecone, fins and body is only a few percent. Base drag accounts for around 20%. It is clear,therefore, to improve the aerodynamic performance of a LoPer class rocket, it is worthwhile to reduce friction drag. This can be achieved by striving to have a smooth finish on the body and fins. This serves to reduce boundary layer thickness and helps promote laminar flow, both of which reduce frictional drag. One also notes that choice of nosecone (shape) will not make much difference, as nosecone drag is minimal. The other significant component is base drag, Adding a boattail can greatly reduce base drag at low mach numbers. Interference drag accounts for approximately 10% of the total drag. Fairing the fin/body joint can be effective in reducing interference drag.
As mentioned earlier, at low subsonic speeds, air behaves as if it were an incompressible fluid. Above approximately Mach 0.7 however, compressibility effects (air flow density variation) start to appear. If our subsonic rocket were pushed beyond sonic velocity, drag starts to increase dramatically, as shown in Figure 2, rising to a peak at just over Mach 1. The drag coefficient (and therefore drag force) approximately doubles.
Figure 2: Drag coefficient for a subsonic rocket
As such, MiPer class EX rockets, which are designed for the "transonic" flight regime (up to Mach 1), greater care is necessary with regard to aerodynamic design. For example, choosing an appropriate nosecone shape can make a big difference. If the conical nosecone used for the subsonic rocket is swapped out for a tangent ogive nosecone (shown here ), the rocket drag coefficient improves signficantly in the transonic region of flight. This is illusrated in Figure 3.
Figure 3: Drag coefficient for a transonic rocket
MiPer class EX rocketss can be quite similar in design to LoPer class EX rockets with a simple aerodynamic change such as nosecone shape. Structural loading is higher due to greater drag in the transonic region (even with a suitable nosecone shape) due both to the drag coefficient and higher maximum velocity (and therefore higher dynamic pressure or "MAX Q"). This needs to be taken into consideration.
For HiPER and ViPER class rockets, aerodynamic considerations are of particular importance due to the high velocities involved and the potential for high drag loads. Figure 4 shows drag data for a typical supersonic (HyPer class) rocket (shown here ). The graph on the left shows the drag coefficient for the various components that make up the total drag coefficient. The graph on the right breaks down the percentage of total drag for the various drag components
Figure 4: Breakdown of drag for a supersonic rocket
For this particular rocket, base drag rises dramatically as the sonic barrier is breeched, in fact, accounting for nearly 50% of the total drag. The percentage decays at higher mach numbers, reaching about 37% at mach 3. Skin and fin frictional drag become less relevant as the mach number grows. Base drag can be reduced with careful design of a boattail. A boattail is a tapered fairing mounted at the aft end of the rocket (shown here ). The design of the aft end of the boattail is of course limited by the nozzle exit diameter. Figure 5 illustrates the difference in rocket drag coefficient for a rocket without and with a boattail. One thing to note is that the addition of a boattail has a destabilizing effect. The normal-force coefficient for a boattail is negative, which means that the boattail tends to shift the CP of the rocket forward, compared to a rocket without a boattail. If a boattail is added to an existing design, it is important to recalculate CP and the stability margin (see Fin Sizing and Static Stability webpage for details on calculating stability margin).
Figure 5: Supersonic rocket drag coefficient: with/without boatail
Details regarding the aerodynamic design of nosecones and fins are presented in the Nosecone and
Fin Sizing and Static Stability web pages.
Summary
In the preceding discussion, it should be noted that the drag coefficients are for a rocket flying at zero (or small) angle of attack. At zero angle of attack, the rocket is geometrically (longitudinally) aligned to its velocity vector. If a rocket is flying at an appreciable angle of attack, such as due to aerodynamic misalignment of fins, or if flying in a strong cross wind, drag on the rocket increases appreciably. This will not be discussed in detail, as the goal of an EX rocket designer is to design and build the rocket with the goal of having it fly perfectly straight. In reality, things like wind at launch time are hard to control, so the likelihood of achieving 'zero angle of attack' may not be likely. This is one reason why EX rockets (and hobby rockets in general) often do not achieve predicted altitude based on computer sims.
It is worthwhile for the amateur rocket designer to strive for a suitble degree of aerodynamic cleanness. This can be achieved, with reasonable effort, a number of ways:
- Nosecone and fins can be readily designed to minimize drag for the particular flight regime of a rocket.
- Fins should be carefully aligned to the longitudinal axis of the rocket. This will reduce drag by helping to maintain zero angle of attack. As a design consideration, a jig or tool may be used to ensure alignment of attachment to the rocket body.
- To reduce interference drag, the fin-body interface should be faired. Fairing radius should be 4-10% of fin root chord.I have used epoxy-based putty to fair the fins. This also increases the strength of the fin-to-body joint. Using microballoon filler keeps the mass of the putty to a minimum.
- Protruberances should be minimized in size (e.g. launch lugs, camera fairings)to reduce parasitic drag and should be balanced by having pairs, on opposing sides of the rocket, in order to have aerodynamic balance which helps maintain zero angle of attack in flight.
- To reduce frictional drag, fastener heads exposed to the airstream (e.g. for couplers) should be "flush-head" (ideally) or pan-head.
- Rocket body and other components exposed to airstream should have a smooth finish. Filling, sanding and painting are a simple way to achieve this. The rocket needs to be painted, anyway, for visibility and aesthetics, so why not endeavour to achieve a fine finish to the paint job. A fine finish minimizes the boundary layer thickness. boundary layer adds to the effective diameter of the rocket through the displacement thickness, thereby increasing the pressure drag. Secondly, the shear forces at the surface create skin friction drag. Nosecones that are made by 3D printing can be made smooth by a combination of sanding and glazing (automotive spot putty works very well). PLA plastic can be made smooth by the use of sandpaper alone, starting with coarse grit and incrementally working down to fine grit. I typically use the following succession of sandpapers: #120, #220, #400, #600, #800, and finally #1000. Dry sanding is done with the #120 & #220 sandpapers, followed by wet sanding with the subsequent sandpapers.
- Adding a boattail should be considered, bearing in mind its negative effect on stability.
- Although not discussed here, when designing a rocket that flies at higher mach numbers (e.g. > mach 3) aerodynamic heating needs to be taken into consideration for nosecone and fin design.
Thanks goes out to Hans Olaf Toft for his AeroLab software, from which the drag coefficient data was excerpted.
Resources:
Res. 1 Rocketry aerodynamics Rick Newlands (AspireSpace Technical Paper)
Res. 2 TR-11, Model Rocket Technical Report "Aerodynamic Drag of Model Rockets", Dr.Gerald M.Gregorek (Estes publication)
Res. 3 "Missile Configuration Design", S.S. Chin (McGraw-Hill Book Co., Inc.), 1961
Reference [1] :"Small Sounding Rockets - A Historical Review of Meteorological Systems 1955 to 1973" Richard B.Morrow
Next-- Rocket Body Design Considerations
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