JNUK
Well-Known Member
Natural Frequency is a coefficient suggested as one of the useful indicators of a rocket dynamic stability. It is readily computed in RockSim, but it is not available in OR. However, it is possible to calculate the frequency using OR data export. Here is how I do it.
The formula for calculating a rocket Natural Frequency is as follows:
wn=sqrt(C1/IL) (1)
Where:
wn - natural frequency, rad/sec
C1 - corrective moment coefficient
IL - Longitudinal Moment of Inertia, kg*m^2
IL is computed by OR , but C1 is not directly available. To compute C1 the following formula is to be used:
C1= (V^2)*Aref*Cna*(Z-W)*p/2 (2)
Where:
p- density of air, approx 1.24 kg/m^3
V- velocity of the rocket (Total velocity of rocket in OR), m/sec
Aref - reference area, m^2
Cna - normal force coefficient
Z- CP of the rocket , m
W - CG of the rocket, m
In (2) V, Aref, Z and W can be directly obtained from OR. Cna can be calculated as follows:
Cna= Cn/alfa (3)
Where:
Cn - Normal force coefficient as it is calculated by OR
alfa - Angle of attack, rad
In (3) both Cn and alfa can be obtained from OR. It has to be noted that (3) is a valid approximation for small angles of attack.
Summarising, the following variables have to be exported from OR (pay attention to units)
In Excel:
Using (3) calculate Cna
Using (2) calculate Corrective Moment Coefficient C1
Using (1) calculate Natural Frequency
Any comments are more than welcome. My next step is to work out how to obtain Damping Ratio.
The formula for calculating a rocket Natural Frequency is as follows:
wn=sqrt(C1/IL) (1)
Where:
wn - natural frequency, rad/sec
C1 - corrective moment coefficient
IL - Longitudinal Moment of Inertia, kg*m^2
IL is computed by OR , but C1 is not directly available. To compute C1 the following formula is to be used:
C1= (V^2)*Aref*Cna*(Z-W)*p/2 (2)
Where:
p- density of air, approx 1.24 kg/m^3
V- velocity of the rocket (Total velocity of rocket in OR), m/sec
Aref - reference area, m^2
Cna - normal force coefficient
Z- CP of the rocket , m
W - CG of the rocket, m
In (2) V, Aref, Z and W can be directly obtained from OR. Cna can be calculated as follows:
Cna= Cn/alfa (3)
Where:
Cn - Normal force coefficient as it is calculated by OR
alfa - Angle of attack, rad
In (3) both Cn and alfa can be obtained from OR. It has to be noted that (3) is a valid approximation for small angles of attack.
Summarising, the following variables have to be exported from OR (pay attention to units)
- Time, sec
- Normal force coefficient
- Angle of attack, rad
- Total velocity of rocket, m/sec
- Reference area, m^2
- CP of the rocket , m
- CG of the rocket, m
- Longitudinal Moment of Inertia, kg*m^2
In Excel:
Using (3) calculate Cna
Using (2) calculate Corrective Moment Coefficient C1
Using (1) calculate Natural Frequency
Any comments are more than welcome. My next step is to work out how to obtain Damping Ratio.
