


NERO Projects H8 Rocket Aerodynamic design  
The H8 Aerodynamic design 












After the decision to go for a rocket with a limited lifting surface
control the first question arises: what kind of configuration do we like. There are several possibilities:
Canard control is a small lifting surface in the front area of the rocket. This means that a positive deflection or rotation of the canard (positive about the outgoing hinge axis of the right canard looking in forward direction of the rocket) the induced aerodynamic force contributes to the main lift vector of the rocket. Wing control is generally a larger lifting surface in the neighbourhood of the centre of gravity of the rocket. Advantage is that the main liftvector can, more or less, directly be canted. However, since the forces are stronger, for the aerodynamic lift of the rocket, the accuracy of the control is much more sensitive. Moreover, due to these forces the hingemoments might be more significant so that a powerful wingcontrol system will be required. In case of a tailfin controlled configuration the deflection of the surface will cause an aerodynamic force that will be in opposite direction with respect to the main lift vector, since the tailfin is at the rearward side of the centre of gravity. This means that the aerodynamic force of the tailfin should acting in a reversed direction compared with the canard at the front, in order to affect the same rotational motion of the rocket. Since in case of the tailfin controlled configuration, space is required to buildin the actuators, while at the same time the space would be necessary for the available propulsion system, it was decided to skip the tailfin option. For the wing controlled option the risk of having serious deviations in the main vector is much bigger than in case of the canardconfiguration. Therefore in the first assessment process the canardcontrolled configuration was selected 






Now we decided on the type of configuration, it will be time to select
some requirements that the rocket should fulfil. These are:







Assuming a stability margin of about 1 is a direct indication for the
rocket design. Since the pitching moment M is linear dependent on the normal force N we will have the following
relation:
where x_{cp} and x_{cg} are, respectively, the distance x of the centres of pressure and gravity on the body axis with respect to the body nose. Describing the forces and moments in terms of coefficients without dimension: and with r and v respectively, the air density and velocity, while S_{ref} and L_{ref} are the reference surface and length, the relation between pitching moment coefficient C_{m} and normal force coefficient C_{N} becomes: Roughly for small angles of attack these coefficients are linear dependent with the angle of attack. This can be expressed by using the derivatives to the angle of attack a : and So we obtain the relation: From this relation it is easy to see, that when the static margin is in the order of 1 and
(using L_{ref} as the body diameter) that: Going back to the design criterion, that the static margin is about 1, then we see that this implies for small angles of attack that the derivative of the pitching moment coefficient must have the negative value of that of the normal force coefficient. However, since the normal force as function of the angle of attack is mainly dependent on the body geometry including a first ‘guess’ of the tailfins and the canards, a first order of magnitude for the required pitching moment coefficient can now be obtained. By decreasing or increasing the tailfin surface, the relation between C_{m}a and C_{N}a can be finetuned. During this iterationprocess the canard surface should be kept constant. Via this process a first estimation of the tailfin configuration has been obtained. A next step will be the dimensioning of the canard surfaces. 






In order to derive the geometry of the canard we will look at the
trimmed conditions of the rocket. The rocket will be trimmed when at a certain angle of attack the deflection of the
canard is such that the resulting pitching moment is zero. So that, in such case, the rocket will intend to keep its
angle of attack without being forced to rotate.
Again, assuming that for small deflection angles the influence of the generated pitching moment is linearly dependent on the canard deflection we can determine the relation for the C_{m} as follows: where d stands for the canard deflection and C_{m}d is the derivative of the pitching moment coefficient to the canard deflection. Now, based on the criterion that in a trimmed condition the resulting pitching moment should be zero (C_{m}=0), we will obtain a relation between the trimmed deflection as function of the angle of attack: Since we have expressed the requirement that the relation between (trimmed) deflection and angle of attack should be in the order of 1 or 2 it is clear that the last equation will prescribe a relation between C_{m}a and C_{m}d . For instance assuming that this relation is about 1 (d _{t}/a _{t} » 1) than Again this is a clear criterion to dimension the surface of the canard. 






Using the foregoing process as a guideline then we have obtained a
configuration of which the body geometry is shown below.
In addition the curves for the normal force and pitching moment coefficients are given as function of the angle of attack a . The calculation of the aerodynamic coefficients are based on Mach = 0.6, while L_{ref} = 0.1 m, being the body diameter, S_{ref} = 0.00785 m^{2} is the body crosssection, and x_{cg} = 0.838 m with full motor mass and body length of 1.38 m. For comparing the result with the applied process we obtained the following estimations of the aerodynamic values:
Note that these values are based on nonlinear effects of the aerodynamic coefficients. A final design will only be obtained in several iteration loops. 




