Suppose that I have found the solution of an optimal continuous thrust planar orbit transfer from circular orbit A to orbit B by means of a numerical method. It's considered that the mission must be done in a fixed final time and the performance index is to minimize the magnitude of the commanded acceleration to the spacecraft. After solving the problem, I have the optimal time histories of the accelerations, tangential and normal to velocity vector.
- How can I compare the performance of the solution with an equal Hohmann transfer?
- Is that a good idea to compare a two impulse transfer with a continuous thrust one?
- Theoretically, I think that continuous thrust transfers must have better efficiency with respect to a limited two impulse transfer; is that correct?
- How can I calculate Delta-v for this problem; by simply integrating the magnitude of the acceleration command vector?
Hi, with a continuous thrust you need to integrate the mass equation. Indeed the mass m varies according to dm/dt=-F/g0/Isp where F (N) is the thrust modulus, Isp (s) is the specific impulse of the engine and g0=9.80865 ms-2. The DV of the transfer can be computed as DV=g0.Isp.ln(m0/mf) where m0 and mf are the initial and final masses. The Isp of electrical engines is High compared to that on chemical ones leading to small fuel consumptions but the transfer time is long.
Richard Epenoy Hi, many thanks for your answer. But I am interested in comparing the efficiency of the continuous thrust acceleration command with the ideal Hohmann transfer regardless of the Isp of these two different types of propulsion systems. Actually, I want to know that continuous application of thrust is better or impulsive application, from theoretic and mathematical point of view.
- I have chosen the transfer time of the continuous thrust equal to the Hohmann's transfer time.
- I have neglected the mass equation from the problem.
- The optimisation is performed numerically for continuous transfer.
Hi, what is your performance criterion for the continuous transfer? fuel consumption?
Richard Epenoy yes, the integrand of the performance index is acc_n^2+acc_t^2. acc_n is the normal and acc_t is the tangential commanded acceleration (with respect to velocity vector).
Hi Mehdi, the square of the norm of the acceleration does not correspond exacty to the DV. Even when considering a constant mass, the correct integrand is the norm of the acceleration (without the square).
Hi dear Richard Epenoy , I am going to change the performance index and perform some numerical simulations; then I'll give the results in the following answers to this question as soon as possible. Many thanks for your help.
First of all, I would like to point out that in fact, Hohmann transfer is not a good maneuver for orbital transfer in a real case. This is because Hohmann transfer is a 2-impulse maneuver that can not take into account space perturbations and will obviously miss the mission in the long run.
Next, I have to point out that unlike Hohmann transfer, low-thrusr is a good maneuver for real cases.
Finally, you can focus on comparing the required velocity change of the maneuvers and compare them.
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