4262: Rockets and Mission Analysis Assigned: October 25, 2016
Homework #4 Due: November 8, 2016
Purpose of Assignment: Electric rockets represent an advanced propulsion system which is highly relevant today for deep space propulsion.
Part 1: Read Chapter 14 in Mechanics and Thermodynamics of Propulsion, by Philip Hill and Carl Peterson, which provide excellent practice in becoming more familiar with electrostatic propulsion, and in particular ion propulsion.
Part 2: Answer problems 14.1 – 14.9.
Part 3: Answer the following additional questions to address electric propulsion in the context of modern contemporary issues/challenges that are faced in this area of rocket propulsion.
14.1: With a charge to mass ratio of 500 C/kg, the required acceleration voltage is about 9x105 Volts. What are your thoughts on this number, is it prohibitively large? The problem states, “An electrostatic rocket is to use heavy particles…”. If the ions are singly charged, how heavy are these particles in kg? Assume that the mass of the power supply scales linearly with the voltage (which is not exactly true, but good enough for this question). If the specific mass of this thruster, a, is 30 (See Figure 10.12), how massive is the power supply? Compare this with a more reasonable value of Va of 1,000 V for a 1.6 kW thruster.
14.2: In part (b) we find that the power per unit thrust is about 24,500 W/N. What is this value for the Space Shuttle Main Engine (SSME)?
14.3: Is 5 N a typical value for electrostatic (ion) thrusters?
14.4: Show that dv/dt = u(dv/dx) for this problem.
14.5: The thrust per unit area for this rocket is 0.0609 independent of if the propellant is Cs, Hg, or Xe. If each of these propellants cost the same amount and each was equally as easy to handle, is there a reason to choose one above the rest? What is the thrust per unit area of the SSME?
14.6: Compare the results of this problem with Figures 14.6 and 14.7.
14.7: The result of this problem suggests that the thrust per power of the propellant is independent of the spacing between the grid, L. Does this make sense?
14.8: How does the result of this problem compare with Equation 14.10?
14.8 (Optional): Compare and contrast a Hall effect and Kaufman ion thruster.
14.9: The result of this problem is a loss of 248 eV/ion, and an estimate made on this number is 100 eV/ion in Section 14.2 of the text. How much would the efficiency change if the loss were 100 eV/ion, i.e. how sensitive is the efficiency to loss/ion?
Part 4: Extend Problems 14.1 – 14.9 in some innovative way that you feel will add to the value of the problem, and makes the problem more interesting and relevant.
1