Propulsion - Purdue University



4. Propulsion

4.1 Launch Vehicle

The Daedalus, in both the MSP and OSP configurations, will use the Delta IV-Heavy as its launch vehicle. NASA’s OSP request for proposal demanded the use of either the Delta-IV or Atlas-V Evolved Expendable Launch Vehicle. Both vehicles have been designed in more than one configuration based on customers’ lifting performance requirements. Along with the Lockheed’s Atlas V-H configuration, Rocketdyne’s Delta IV-H possesses the largest payload lifting capability of any currently manufactured launch vehicle. It was quickly agreed upon that in order to maximize the capabilities of the space plane a maximum weight limit would be needed. Table 4.1 compares the two vehicles. The slightly better lifting performance of the Delta IV-H coupled with its higher technological standard made it the best candidate for launching Daedalus.

| |Atlas V Heavy |Delta IV Heavy |

|Payload to 90( |19,000 kg |20,800 kg |

|Cost |$140-170 million |$140-170 million |

|Launch Sites |Vandenberg/ |Vandenberg/ |

| |Cape Canaveral |Cape Canaveral |

|Booster Stage |RD-180 (2) |RS-68 (2) |

|First Stage |RD-180 |RS-68 |

|Second Stage |RL10A-4-2 |RL10B-2 |

Table 4.1: Comparison of Atlas V and Delta IV EELV

The stringent reaction and turn-around times demanded by the Department of Defense for the MSP design would automatically disqualify both the Atlas and Delta rockets, which rely on cryogenic propellants in all their stages. The only storable heavy launch vehicle with the requisite capabilities is Lockheed’s Titan IV-B. The vehicle is currently out of production and only a handful remains to be launched. Zero boil-off technologies in cryogenics are in a state of advancement. However, most research has been done on scales much smaller than that of an all-cryogenic vehicle. Due to this dilemma it was decided that, for the sake of trajectory analyses, the Delta IV-H would also be used to boost the MSP mission.

4.2 Boost Trajectory

The trajectory analysis was done for two different target orbits: for the OSP, the orbit of the International Space Station and for the MSP, a 185km polar orbit. The computer code that was used to perform the analysis was written in FORTRAN. Although codes from previous semesters were available for modification, the Daedalus code was written from scratch in order to gain a better understanding of the launch trajectory analysis.

4.2.1 Vehicle Equation’s of Motion

The boost trajectory for the Delta IV-H is based on the equations for flight derived in Chapter 2 of Vihn’s Hypersonics (Appendix D1: Eqs 1-6). Vihn defines the vehicle’s trajectory with respect to a rotating Earth, the axes through the center of rotation of which form the inertial frame of reference. The method for determining the boost trajectory consists of plotting an uncontrolled trajectory or ‘ideal trajectory’ from the launch point to the target orbit with the assumption of no cross-winds. The plotting of this trajectory requires a systematic variation of variables until the required solution to Vihn’s equations is reached. The cross-winds are then factored into these equations and the thrust of the vehicle is vectored to negate any deviation from the ideal trajectory. Vihn divides his equations into two groups of three, namely the force equations and the kinematic equations. The force equations (Appendix D1: Eqs 1-3 ) define the rate of change of velocity, flight path angle and heading angle which are dependent on the dominant forces acting on the vehicle specifically the vehicle’s thrust, aerodynamic forces of lift and drag, and the force of gravity. For the case of a rocket, the coefficient of lift is negligible and thus also the force of lift. Also, thrust vectoring is assumed only to be a means for counteracting trajectory disturbances due to winds during the low altitude portion of flight. Hence they are neglected until the factoring in of cross winds. The terms containing the angular velocity of the Earth are the Coriolis terms and, although negligible for most cases, they should be retained for an accurate analysis. The kinematic equations (Appendix D1: Eqs 4-6) relate the motion of the vehicle to spherical coordinates. They allow the position of the vehicle to be tracked as a function of its altitude, latitude, and longitude. To account for mass variation as propellant leaves the vehicle, the mass flow rate equation is added to the system (Appendix D1: Eq 7)

The simultaneous solutions of these ordinary differential equations with respect to time provide the values necessary to define the trajectory of the vehicle. These equations are solved in FORTRAN with the help of a subroutine entitled ‘RK4.F’, which is based on the Runge-Kutta numerical method of integration. Before an accurate solution can be obtained from these equations, the proper initial conditions of the trajectory must be defined.

4.2.2 Initial Conditions

The simultaneous solution of the differential equations of motion requires the use of proper initial conditions. As the ideal trajectory must have no control interference, the path of the vehicle is dependent solely on the user’s choice of initial conditions. While initial conditions of latitude and longitude are preset by the location of the launch site, the vehicle’s initial flight path angle and heading angle must be varied in order to achieve the required final solutions. Also, a proper variation in the vehicle’s thrust profile is integral to attaining the required orbit.

4.2.3 Final Solutions

The target orbit is assumed to be circular at the required altitude. Hence the velocity needed to remain in the orbit can be calculated simply from the altitude and Appendix D: Eq 8. The inclination of the orbit is given by Appendix D1: Eq 9, which is dependent on the vehicle’s heading angle and latitude. Both these angles are output from the code. Hence, the goal of the trajectory code is to end up with the proper velocity, altitude, and inclination angle.

4.2.4 Constant Flight Path Trajectory

As general equations of atmospheric reentry flight, Vihn’s equations were derived for the purpose of defining the trajectory of a body moving with a ‘high’ velocity for its entire trajectory. A ‘high’ velocity refers to one which prevents the negative gravity term in Appendix D1: Eq 2 from dominating the equation for the rate of change of flight path angle. Neglecting aerodynamic forces and the Coriolis terms, Appendix D1: Eq 2 reduces to Eq 10,

[pic] Eq 10

For the case of a zero initial velocity, analytically we see that the gravity term in Eq 10 tends toward negative infinity resulting in an instantaneous decrease of the flight path angle immediately after launch. By the time the velocity is high enough to counteract the gravity term, the direction of the velocity vector is already reversed and pointing toward the Earth. To avoid this unintentional low-altitude gravity turn it is necessary to define the trajectory of the vehicle through alternative means up to a velocity that Vihn’s equations can handle.

Vihn derives a linear equation to determine the velocity of a vehicle at the end of a specified burn time. This equation is based on the familiar ‘rocket equation’ (Appendix D1: Eq 11) and assumes a constant flight path angle while neglecting Coriolis effects. Although Eq 11 is a simple approximation, it is used for a very small portion of the trajectory and thus will not affect the overall trajectory by much. Various burn times were used to obtain a velocity that would serve as a feasible initial condition to Vihn’s equations. The altitude at the end of the burn time is given by Appendix D1: Eq 12.

These equations are used in the start of the main program of the Daedalus boost codes. The minimum time of vertical flight was determined as 30 sec, which is comparable to the 15 sec of vertical flight used in previous boost codes. For a realistic simulation, the constant flight path angle was set to 90°. The velocity and altitude thus obtained are initial conditions for Vihn’s equations.

4.2.5 Variable Flight Path Trajectory

After the completion of the linear trajectory, Vihn’s equations are implemented up to the orbital insertion point. The orbital insertion point, which forms the final conditions for the solution to Vihn’s equations, is defined by a velocity, an altitude, and an inclination angle. These were defined earlier. Vihn’s equations are represented in state variable form in a subroutine entitled ‘boostraj’. This subroutine calculates the derivatives of the velocity, flight path and heading angles, altitude, latitude, longitude, vehicle mass, and vehicle stagnation temperature with respect to time. These derivatives are then called by the subroutine ‘RK4’ to be numerically integrated. However, as Appendix D1: Eqs 1-7 indicate, there are many other terms in Vihn’s equations that must be defined before the equations can be solved.

Environmental Data

The boost codes take into account the variation of acceleration due to gravity with altitude using Appendix D: Eq 13. The density and temperature of the atmosphere is defined in the file ‘atmo76.f’, which was provided by Prof. Gustafson, formerly of Purdue University, in the fall of 1997. It contains numerical values for Earth’s atmospheric density and temperature from sea-level up to an altitude of 121.4km and is based on the 1976 standard atmosphere. When called, the program outputs ambient temperature and density with altitude input. It also outputs speed of sound values from ambient temperature using Appendix D1: Eq 14. By assuming an ideal atmosphere, ambient pressure is determined from the perfect gas law (Appendix D1: Eq 15). With the vehicle’s environment defined, the boost code then defines the aerodynamics of the launch vehicle.

Vehicle Aerodynamics

As described earlier, the coefficient of lift term in Vihn’s equations is neglected. However, the vehicle’s drag is too large to be neglected in the ideal trajectory, and is even more necessary when computing the forces due to winds. The subroutine ‘codrag’ calculates the drag coefficient of the launch vehicle with inputs of current velocity, altitude, and atmospheric speed of sound. Appendix D1: Eqs 16-18 determine the drag coefficient from the vehicle Mach number, which is computed from the velocity and speed of sound. They are equations for the drag on a cone and were obtained by Prof. Gustafson from Shapiro’s ‘The Dynamics and Thermodynamics of Fluid Flow’.

Vehicle Surface Areas

The base area of the vehicle is required for calculating its drag. It is computed simply as the largest circular area of the launch vehicle stack. This value is obtained from Isakowitz’s ‘International Space Launch Systems’. For the Delta IV-H this number would be multiplied by three since the two booster stages are identical to the vehicle first stage. The side area is the longitudinal planform area of the rocket components. To analyze the largest wind forces, the largest planform area of the vehicle is used. This is simply three times the planform area of the vehicle components. The tumbling drag of the discarded stages, which will be discussed later, is also dependent on the side areas of each stage.

Thrust Profile

The throttling capabilities of the Delta IV’s first stage motor give us a parameter that can be used to passively control the vehicle. Varying the burn times of each stage and their throttle has a large effect on all the parameters, specifically the rates of change of velocity and flight path angle. The variation of thrust with atmospheric pressure is governed by Eq 19 from G. P.Sutton’s ‘Rocket Propulsion Elements’,

[pic] Eq-19

Assuming negligible exit pressure, the first term represents the vacuum thrust of the engine, which is a constant parameter. Hence, the formula used to vary thrust becomes Eq-20,

[pic] Eq-20

Total Acceleration

The vehicle’s total acceleration throughout its trajectory can be resolved into a tangential and a normal component. The tangential component is the rate of change of tangential velocity, or in other words, the value of the velocity derivative from Vihn’s equations. The normal component of acceleration is given by Appendix D1: Eq-21, which was obtained from the Fall 2000 code.

Wind Forces

The winds and gimbal angle are set to zero for the ideal trajectory. However, in reality, the forces due to winds can have a large effect on trajectory as they occur at low altitudes. The vehicle is moving relatively slow at these altitudes and is thus more susceptible to deviation. The subroutine ‘windy’ is used to calculate the tangential and normal forces due to winds at the launch site. These forces are then included in the force equations of Vihn’s equations. The subroutine is a modified version of a subroutine of the same name taken from Prof. Gustafson’s ‘boost.for’ (Summer 1998) and last modified by Shannon Fitzpatrick (Fall 2000). It requires the definition of the variation of wind velocity with altitude over the launch site. Wind velocity at various altitudes over Cape Canaveral and Vandenberg is contained in a report provided by Prof. Gustafson, although the source of the report is currently unknown. This data is curve fit into a quadratic equation using the Matlab file ‘winds.m’ (Appendix D2). For higher order polynomials the equation is much less accurate. At each increment of the non-ideal trajectory ‘windy’ is given the altitude of the vehicle along with its flight path and heading angles. Using this data, along with the drag coefficient and side area of the vehicle, the subroutine determines the normal and tangential wind forces on the craft. Along with the ideal solutions, the wind-affected solutions with zero gimbal angle are determined.

Gimbal Control

The thrust vectoring of the first and booster engines of the Delta IV-H must be implemented to counteract the effects of the wind forces. The ideal trajectory is maintained by stabilizing the flight path angle of the vehicle. This is achieved by using a proportional-derivative feedback controller as in Fig 4.1.

[pic]

Fig 4.2: Proportional-Derivative gimbal control

In this case, the control force is the gimbal angle and the error is the difference between the ideal and non-ideal flight path angles. The proportional and derivative gains must be varied until a minimum error is attained throughout the wind-affected portion of flight. Information regarding the maximum gimballing angle for the Delta IV’s first stage could not be found. However, the angles must be kept to a minimum in order to ensure that the tangential thrust does not get depleted and the vehicle does not lose velocity. A range of 3-4° will typically prevent too much thrust from being lost.

Discarded Stage Trajectory

The trajectories of the discarded stages are determined much in the same way as the launch vehicle. The boost code keeps track of the solutions to Vihn’s equations for the times at which the stages separate from the main vehicle. These solutions form the initial conditions for the discard trajectories. The thrust for the discard stages is assumed to be zero while the mass is assumed to be constant, i.e. the stages remain intact. Also, the trajectories of the two boost engines are assumed to be identical. The drag on the inert stage component is a combination of the regular base drag as well as the side drag of the stage. The drag is analyzed using a crude tumbling model given by Appendix D: Eq 22. The code then solves Vihn’s equations for each discarded stage.

4.2.6 Boost Trajectory Analysis

Boost trajectories were determined for the two different OSP configurations and the MSP configuration using the defined methods. The mission target parameters for the vehicles are outlined in Table-4.2.

| |Daedalus 1 |Daedalus 2 |Daedalus 1M |

|Vehicle Mass (kg) |22,214 |23,203 |20,787 |

|Inclination (°) |51.6 (ISS) |51.6 (ISS) |90.0 |

|Velocity (m/s) |7,670 |7,670 |7,790 |

|Altitude (m) |400,000 |400,000 |185,000 |

Table 4.2: Boost trajectory missions

Daedalus 1 Results

[pic][pic]

[pic][pic]

[pic][pic]

[pic]

[pic]

[pic][pic]

[pic][pic]

[pic]

Daedalus 2 Results

[pic][pic]

[pic][pic]

[pic][pic]

[pic][pic]

[pic][pic]

[pic][pic]

[pic]

Daedalus 1M Results

[pic][pic]

[pic][pic]

[pic][pic]

[pic]

[pic]

[pic][pic]

[pic]

[pic]

4.3 Reaction Control System

4.3.1 RCS Thrusters

According to G. P. Sutton’s ‘Rocket Propulsion Elements’, a total of 12 thrusters are required to ensure complete maneuverability using the application of pure torques about three axes. The RFP requires double redundancy in the RCS, and as a result, the OSP is required to be fitted with a total of 24 thrusters. The selection and position of the reaction control thrusters is ultimately dependent on their ability to turn the spacecraft 180° along its yaw axis within the time period between the end of the de-orbit burn and the time at which the craft reaches the Earth’s atmosphere. This time period is given by Appendix D1: Eq 23. The force term in this equation is the thrust of a pair of rockets involved in the turning maneuver separated by the length term. The moment of inertia term is along the axis of rotation and is an output of the CAD program used to model the spacecraft and its components. By varying the separation distance, the time taken for a pair of thrusters to turn the vehicle about an axis can be determined. The Matlab script ‘RCS.m’ was used to plot the variation of rotational time periods with thruster separation distance for Rocketdyne’s RS-25 thruster. This thruster has a comparatively high thrust output (111 N) for a small weight (0.96 kg). The shuttle RCS thrusters were found to be heavier with a high thrust output beyond the needs of the Daedalus.

[pic]

Figure 4.3.1.1: RCS Yaw Time Period for Daedalus

The yaw time period denotes the time taken for the craft to complete a 180° turn after the de-orbit burn. The de-orbit trajectory analysis revealed a total time period of about 32 min (1920 s) between the end of the de-orbit burn and the start of the atmosphere for the ISS orbit. The time required for the MSP mission is 9.5 min (570 s). Fig 4.3.1.1 shows that as long as their separation distance along the longitudinal axis is greater than 0.055 m, two RS-25’s generate enough thrust to turn the Daedalus 1 within the needed time period. This length is available since the craft is 20 m long. For the Daedalus1M, a minimum separation length of 0.165 m is required to meet its retro-burn recovery window. This is easily done in its 14 m of length. The length required for the Daedalus 2 is also easily attainable.

4.2.2 RCS Fuel, Oxidizer, & Pressurant Tanks

The pressure in the fuel and oxidizer tanks ultimately depends on the required pressures in the combustion chambers in addition to the pressure drops between the chambers and the tanks. This is represented by Eq-24.

[pic] Eq-24

Since 2 thrusters are fired to start the rotation of the vehicle about a single axis and 2 opposite thrusters are subsequently fired to stop the motion of the vehicle about that axis, we can assume that no more than 6 thrusters are fired simultaneously. So the pc term need not be greater than six times the chamber pressure of a single RCS thruster. Also, assuming radiation cooling, the pressure drop due to regenerative or film cooling techniques are non-existent. Using the following values based on data provided in class for the RS-25 and values suggested in Humble the required tank pressure was determined.

[pic]

Now that the pressure in each tank is known, the volume of liquid in each tank must be determined. The O/F ratio for the RS-25 thruster is 1.6. Hence, the masses of fuel and oxidizer are given by Eqs-26&27,

[pic] Eq-26

[pic] Eq-27

The volumes are determined from the masses and densities of the propellants as,

[pic]

The total tank volume is the sum of the volume of usable propellant, ullage volume, boil-off volume, and trapped volume (Eq-28).

[pic] Eq-28

Since we are not dealing with cryogenic propellants, boil-off is not a concern. Also, we can assume that the propellant feed system is sufficiently purged of propellants so that there is no trapped volume. Humble suggests a high-end ullage volume of 3% of total tank volume. Hence, Eq-28 becomes,

[pic]

Since these values are close together, the same volume (0.565 m3) will be used for both tanks for the sake of vehicle symmetry and simplicity. Helium was chosen as the pressurizing gas because of its low weight and inertness. The pressurant tank must contain enough gas to completely fill both the fuel and oxidizer tanks at their corresponding pressures. Using the Ideal Gas Law, this means,

[pic]

[pic] Eq-29

The RCS helium tank of the Space Shuttle has a burst pressure rating of 3200 psi (22,063,222 Pa). Using a safety factor of 2.0 as suggested by Humble, this corresponds to a Helium tank pressure of (11,031,611 Pa). The volume of the helium tank according to Eq-29 would then be 0.524 m3. Due to the high pressure of the helium tank, it should be spherical to avoid stress concentrations at edges. Hence the helium tank is a sphere of radius 0.50 m. All three tanks were fit together as close as possible in the arrangement in Fig-6 to minimize pressure losses. The diameter and length of the propellant tanks are 0.5 m and 2.88 m respectively. They were chosen to be cylindrical because of their lower pressures. The materials chosen for the tanks are graphite epoxy with a Teflon lining for propellant compatibility. Graphite-epoxy was chosen for its high allowable stress to weight ratio. The tank thickness formulae for spherical and cylindrical tanks were obtained from Humble (p.271). Table-1 summarizes the tank design for the RCS.

|Tank |Pressure (Pa) |Volume (m3) |Thickness (cm) |Mass inc. Fluid(kg) |

|Helium |11,031,611 |0.524 |0.616 |34.04 |

|NTO |5,130,225 |0.565 |0.287 |789.80 |

|MMH |5,102,125 |0.565 |0.285 |500.97 |

Table 4.3.2.1: RCS tank design summary

4.4 Main Engine & Propellant Feed System

4.4.1 Main Engine

The space plane requires a storable upper stage engine due to the quick reaction time required by the MSP and the long mission durations expected from the OSP, which would make cryogenics unfeasible. Although the Shuttle’s OMS engines are well-proven and would provide the required thrust for orbital and atmospheric maneuvering, the thrust of two OMS engines can be achieved by a single Rocketdyne RS-72 at a higher specific impulse. The specifications of this engine are found in Table 4.4.1.

|Propellants |NTO/MMH |

|Thrust (N) |54,400 |

|Ispvac (s) |338.5 |

|Chamber Pressure (bar) |61.7 |

|Mass (kg) |149 |

|Area Ratio |300 |

Table 4.4.1: RS-72 Storable Upper Stage Specifications

There are essentially two options for the propellant feed system namely the pressure-fed and pump-fed system. Since the main propulsion unit forms a larger system than the reaction control system, the possible benefits with choosing a pump-fed system were explored.

4.4.2 Pump-fed Propellant Feed System

A gas generator system was chosen since an expander cycle requires a regeneratively cooled nozzle and the staged-combustion cycle is too complex for the needs of the RS-72 main engine. In a gas generator system, a small percentage of the total fuel and oxidizer flow is diverted into a hot gas generator (combustion chamber) and the exhaust thus obtained is used to drive the rotors of a turbine, which in turn rotate the impellers of the fuel and oxidizer pumps. The turbine gases are then ejected overboard, sometimes through a nozzle. The process for designing a turbo-pump system, as outlined in Humble’s ‘Space Propulsion Analysis and Design’, involves determining the power available from the turbine, the power required by the pumps, and then varying the mass flow rate into the gas generator until the two powers are equal. The specifications of the RS-72 were used to determine the mass flow rates into the thruster.

The above mass flow rates are for the thruster only and do not include the flow of propellant into the gas generator. The power available from the turbine, based on a first-guess mass flow rate into the gas generator is determined by Appendix D: Eq 30. The turbine inlet temperature was taken as 1100 K as this temperature allows many metals to be used in the gas generator/turbine assembly without the need for cooling passages. Various values for efficiency and turbine pressure ratios are available from Humble. The thermochemical data such as specific heat and specific heat ratio of the turbine gases can be determined from TEP (Thermo-Chemical Equilibrium Program), which is used in AAE 439 and AAE 539 to model the thermochemistry of combustion chambers and nozzles. The O/F ratio of the propellant burned in the gas generator was taken as 0.2 as this corresponds to a chamber temperature of 1100 K in TEP. Using this data, the power available from the turbine for a certain mass flow rate can be determined. The performance parameters of the pump, based on tank pressures of 1.5 times atmospheric pressure and a main engine chamber pressure of 6,170,000 N, are listed in Table 4.3.2.1.

|  |NTO |MMH |

|Total Mass Flow Rate (kg/s) |11.254 |5.547 |

|Pressure Rise [Δp] (Pa) |7,919,000 |7,919,000 |

|Density [ρ] (kg/m3) |1,440 |878 |

|Volume Flow Rate [Q] (m3/s) |0.0078 |0.0063 |

|Pump Head Rise [Hp] (m) |564.74 |926.23 |

|NPSH (m) |7.182 |11.78 |

Table 4.4.2.1: Fuel and oxidizer pump requirements

These parameters allow the pumps impellers to be sized. The design of the impellers is summarized in Table 4.4.2.2.

|  |NTO |MMH |

|Suction Specific Speed [uss] |70 |70 |

|Impeller Rotational Speed [Nr] (RPM) |21,324 |69,780 |

|Pump Head Coefficient [Ψ] |0.55 |0.55 |

|Impeller Tip Speed [ut] (m/s) |99.99 |128.06 |

|Impeller Exit Tip Diameter [D2t] (cm) |8.96 |3.50 |

|Pump Efficiency [ηp] |0.80 |0.80 |

|Pump Power [Preq] (W) |74,565 |60,273 |

Table 4.4.2.2: Pump design parameters

The power balance between the turbine and pumps is achieved for a turbine mass flow rate of 0.5% of the total propellant mass flow rate of the main engine system. The mass of the turbo-pump assembly is determined from Eq-31.

[pic] Eq-31

For a conservative result, the higher values of the empirical values A and B were used. A turbo-pump mass of 40.1 kg was obtained. The mass of the gas generator was determined by using mass estimation methods used in combustion chamber design. The high-end characteristic length for an NTO/MMH combustion chamber is 0.89 m. The actual length of the cylindrical combustion chamber will be determined by the chamber contraction ratio. A typical contraction ratio is 3.0. Hence, the length of the combustion chamber is 0.89 divided by 3.0 or 0.30 m. A high-end value for chamber length to diameter ratio is 2.5, resulting in a chamber diameter of 0.12 m. Again, to be conservative it is assumed that the pressure in the gas generator is close to that in the main combustion chamber. The thickness of the chamber wall for a safety factor of 2 is given by the formula,

[pic]

Nickel based materials such as Columbium are typically used in combustion chamber design and have practical tensile strengths around 310 MPa. The wall thickness found by this method is 0.24 cm. The value may be low as the above formula is purely pressure driven and does not take into account thickness required for proper heat transfer. Using the density of Columbium (8600 kg/m3) the cylindrical gas generator has a mass of 2.8 kg.

For an assumed ΔV of 500 m/s for the OSP maneuvering velocity budget, the mass of propellant required calculated from Eq-11 using the Isp of the RS-72 vehicle main engine is 3,503 kg. Using the same process as in the case of the RCS to determine tank sizes for graphite-epoxy tanks we have the following values for the pump-fed system tanks. For the purpose of comparison with a pressure-fed system, a common radius of 0.5m will be used for the cylindrical propellant tanks.

|Tank |Pressure (Pa) |Volume (m3) |Thickness (cm) |Mass inc. Fluid(kg) |

|NTO |151,988 |1.35 |0.02 |2356.7 |

|MMH |151,988 |1.68 |0.02 |1151.1 |

Table 4.4.2.3: Main engine propellant tanks for a pump-fed system (Daedalus 1)

Total Mass of Pump-Fed System including turbo-pump assembly, gas generator, tanks, and propellant = 3550.7 kg

The velocity budget for the Daedalus 1M is given as 3200 m/s in the Department of Defense RFP. Using the above methods, the tanks for the pressure fed Daedalus 1M are located in Table 4.4.2.4.

|Tank |Pressure (Pa) |Volume (m3) |Thickness (cm) |Mass inc. Fluid(kg) |

|NTO |151,988 |6.66 |0.02 |9,592 |

|MMH |151,988 |5.33 |0.02 |4,681 |

Table 4.4.2.4: Main engine propellant tanks for a pump-fed system (Daedalus 1M)

4.4.3 Pressure-fed Propellant Feed System

A pressure-fed system designed using the same methods outlined for RCS is summarized in Table 4.4.3.1. The burst pressure for the Space Shuttle’s helium tanks is again used for the main engine helium tank. The cylindrical tank radius is taken as 0.5 m for the sake of comparison with the pump-fed tanks.

|Tank |Pressure (Pa) |Volume (m3) |Thickness (cm) |Mass inc. Fluid(kg) |

|Helium |11,031,611 |2.23 |0.99 |148.37 |

|NTO |8,143,000 |1.35 |0.91 |2430.2 |

|MMH |8,114,900 |1.68 |0.91 |1243.4 |

Table 4.3.3.1: Main engine propellant and pressuarant tank for a pressure fed system (Daedalus 1)

Total Mass of Pressure-Fed System including pressurant and propellants and their tanks = 3,822.0 kg

The pressure fed system is 271.4 kg heavier than the pump-fed system. The 500 m/s velocity budget allows as much propellant to be carried on board the Daedalus 1 as possible without exceeding the lifting capabilities of the Delta IV-H. The Daedalus will use the pump-fed system due to its lighter overall weight.

Nomenclature

V = velocity (m/s)

m = vehicle mass (kg)

FT = tangential thrust (N)

g = acceleration due to gravity (m/s2)

γ = flight path angle (rad)

ω = angular velocity of Earth (rad/s)

r = radius of orbit (m)

φ = latitude (rad)

θ = longitude (rad)

ψ = flight heading angle (rad)

ε = thrust vector angle (rad)

D = drag force (N)

T = thrust (N)

σ = roll angle (rad)

FN = normal thrust (N)

L = lift force (N)

c = effective exhaust velocity (m/s)

G = gravitational constant (6.672 x 10-11 Nm2kg-2)

M = mass of the earth (kg)

vo = orbital velocity (m/s)

h = altitude above sea-level (m)

i = inclination angle (rad)

m0 = initial vehicle mass (kg)

t = time (s)

zB = altitude after linear boost (m)

μ = ratio of instantaneous mass and initial mass of vehicle

as = speed of sound (m.s)

pa = ambient pressure (Pa)

ρa = ambient density (kg/m3)

Ta = ambient temperature (K)

Rair = gas constant of air (280 J/kg/K)

cd = coefficient of drag

M = Mach number

re = radius of Earth (m)

Ab = vehicle base area (m2)

As = vehicle side area (m2)

θrcs = angle of rotation due to RCS (rad)

Im = mass moment of inertia of vehicle (kgm2)

l = perpendicular separation distance between lines of actions of thrust

ηT = turbine efficiency

cp = specific heat constant of turbine gas (J/kg.K)

Ti = turbine inlet temperature (K)

ptrat = turbine pressure ratio (inlet/exit)

k = specific heat ratio

Appendix D1

Force Equations (Eqs 1-3)

[pic]

[pic]

Kinematic Equations (Eqs 4-6)

[pic]

[pic]

[pic]

Mass Flow Rate Equation (Eq 7)

[pic]

Orbital Velocity (Eq 8)

[pic]

Orbital Inclination (Eq 9)

[pic]

Linear Velocity (Eq 11)

[pic]

Linear Altitude (Eq 12)

[pic]

Variation of Gravity (Eq 13)

[pic]

Speed of Sound (Eq 14)

[pic]

Perfect Gas Law (Eq 15)

[pic]

Drag Coefficient for Cone (Eqs 16-18)

[pic]

Normal Component of Acceleration (Eq 21)

[pic]

Tumbling Drag (Eq 22)

[pic]

Time Period for RCS Turn (Eq 23)

[pic]

Turbine Power Requirement (Eq 30)

-----------------------

Vfinal = 7,603 m/s m/s

³final = 3.04°

¨final = 22.53°

afinal = 399,800 m

µfmax = -1.67°

Final Latitude = 47.50° N

Final Longitude = 47.05° W

Core (Green):

51.12° N, 21.48° W

Boosters (Rγfinal = 3.04°

Ψfinal = 22.53°

afinal = 399,800 m

εfmax = -1.67°

Final Latitude = 47.50° N

Final Longitude = 47.05° W

Core (Green):

51.12° N, 21.48° W

Boosters (Red):

39.68° N, 66.07° W

Main Vehicle (Blue):

47.50° N, 47.05° W

Gimbal

Delta IV

γideal

γ

γideal - γ

ε = kp(γideal – γ) + kd(d/dt(γideal – γ))

+

+

_

[pic]

[pic]

[pic]

[pic]

Vfinal = 7,777 m/s m/s

γfinal = 0.43°

Ψfinal = 270.1°

afinal = 188,266 m

Final Latitude = 10.04° N

Final Longitude = 120.31° W

Core (Green):

4.63° S, 120.32° W

Boosters (Red):

20.17° N, 120.35° W

Main Vehicle (Blue):

10.04° N, 120.31° W

Total Gmax = 5.34

Axial Gmax = 5.31

Total Gmax = 4.89

Axial Gmax = 4.86

Vfinal = 7,614 m/s m/s

γfinal = 3.17°

Ψfinal = 22.21°

afinal = 408,408 m

εfmax = -1.70°

Final Latitude = 47.86° N

Final Longitude = 46.66° W

Core (Green):

51.12° N, 20.85° W

Boosters (Red):

39.71° N, 66.00° W

Main Vehicle (Blue):

47.86° N, 46.66° W

Total Gmax = 4.90

Axial Gmax = 4.88

[pic]

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download