ROCKIIT FINAL PROJECT BRIEFINGCordarryl Solomon-WilliamsFrancisco FloresDaryl VittalDavid FinolGhazi MuhammadOmar AbuosbieYup Zeng

Overview- Final fuel selection- Material Selection- Mission Cost - D-K Charts- Sizing - Dimensions- Ascent Simulation- STK Orbital Simulation- Results- Feasibility of Design- Summary/Conclusion

Fuel SelectionRP-1 and LOX are using for all three stage for reasons below:

• Can provide 322 sec specific impulse which meets our requirement

• Has been used in many spacecraft like Falcon 1e, Delta 3 and Atlas MA and have good record

• Cleaner than most alternatives

• Relatively cost effective. According to NASA record,$0.16/kg for LOX and $0.20/kg for RP-1,which means our cost in fuel will be less than $1,000

Fuel Selection - Pros & Cons Pros

• Liquid Oxygen and RP-1 less toxic• High efficiency • RP-1 easy to store and easy to produce• RP-1 more stable

Cons• Liquid Oxygen, if placed in contact with organic

materials, it may cause fire or an explosion• Containment of Liquid Oxygen costly and complex due

to low temperatures

MaterialsTitanium (grade 5) was chosen as the primary material for

the launch system

Many advantages with this material including-High temperature resistance -High specific strength-Corrosion resistance -Crack resistant

Its main disadvantage is that it is difficult to machine, and therefore is very expensive.

-One manufacturer sells titanium sheets from $15-$25 per kg

Types of Mission CostsA three stage system is complex (the more stages makes the system more complicated)

-This adds cost, after three stages, the complexity is not worth the small initial mass decrease it would generate

Titanium- As previously mentioned, can be bought from $15-25/kg. (~$23,400) Manufacturing costs would also need to be added to this.

Fuel- $0.16/kg for LOX and $0.20/kg for RP-1. (~$900) Cost of tanks would need to be included as well.

D-K ChartsStage 1

D-K ChartsStage 2

D-K ChartsStage 3

Rocket Sizing

Rocket Characteristics: Fuel TanksStage 1:Height-6mDiameter-1.15m

Fuel:

Height-2.85

Diameter-.85mOxidizer:

Height-3.15m

Diameter-1.15m

Stage 2:Height-3.27mDiameter-.73m

Fuel:Height-1.54

Diameter-.54mOxidizer:

Height-1.73m

Diameter-.73m

Stage 3:Height-1.8mDiameter-.46m

Fuel:

Height-.84m

Diameter-.34mOxidizer:

Height-.96m

Diameter-.46m

Rocket Characteristics: NozzleParameters Stage 1 Stage 2 Stage 3

E 75 18.75 18.75

Ae (m^2) 2.011 0.502 0.502

De (m) 1.60015 0.8 0.8

At (m^2) 0.026813 0.026813 0.026813

Dt (m) 0.184768 0.184768 0.184768

theta (degree) 17.2152 17.5223 17.5223

Length (m) 2.28 0.97442 0.97442

Nozzle EfficiencyStage 1: K = TitaniumPower = 367461 WActual Heat loss = 335881 WNozzle Thermal Efficieny: 91.4%Exergy : 87.96% Stage 2 & 3:Power = 628993.43 WActual Heat loss = 597413.63WNozzle Thermal Efficiency: 94.9%Exergy: 94.7%

Exergy (vaccum) Ideal

Rocket Characteristics: Chamber

Stage 1 Stage 2 Stage 3

Length (m) 0.032784 0.08136 0.204901

Diameter (m) 1.15 0.73 0.46

Volume (m^3) 0.034053 0.034053 0.034053

Thickness (m) 0.003389 0.002152 0.001356

Mass (kg) 50.81591 13.6043 4.429881

Rocket Characteristics: InjectorsElectrospray Injector System

● No need of pressure drop along the injector plate● Low power consumption● Extremely small droplet● Active control on mass flow rate and droplet size

(throttling control and active instabilities control)

Advantages:

Other Important Considerations:

Principles of Operation: ● Consists in breaking up the a liquid source into fine

droplets at the end of a capillary through the application of an electric field.

● The droplet size is related to mass flow rate by a power law● The nozzle array and the electrode are connected to a

voltage source to create a strong electrical potential

● Unknown is the effects that the charged droplets will have on combustion

● Also how this kind of injector will work with an applied pressure drop and if this will still be required to prevent the propagation of combustion instabilities upstream hence further theoretical and experimental work is required.

ModelComponents● Fuel tank● Oxidizer tank● combustion Chamber● Nozzle● Outer casing

Ascent SimulationAssumptions:

-Low thrust vector angle (alpha) to induce gravity turn(pitch over)

-Neglect transverse drag-Air density assumed to be rho = 1.225e-9.678065e-5

hkg/m^3-Arc travel assumed to be vertical and horizontal.

(Curve large enough to be considered in North East

Coordinates)

Ascent Simulation

Drag increases parabolically until pitch over around 75s. There is a discontinuity do to rough change of alpha.

Ascent Simulation

Burnout velocity is 7.94 km/s (A bit over our target since we overshot the gravity, drag and steering approximation).

Ascent Simulation

Maximum altitude reached in the simulation is 165.89km (a bit over due to the overshoot in velocity)

Ascent Simulation

Total horizontal distance traveled in the simulation was about 35.16km.

Orbital Parameter Identification and STK Simulation

Given the requirement of a sun-synchronous orbit with an altitude of 165km, it is then possible to derive the period of the orbit, its angle of inclination and RAAN. These can be determined by first setting the orbital precession rate equal to 360 degrees per sidereal year, taking into account the earth’s oblateness effect.

We know the orbital angular precession is: adding the orbital period, then

Finally we can simply find the orbital inclination as a function of the orbital period by:

STK SimulationThe orbital semimajor axis, argument of perigee and eccentricity can be easily derived from its circular nature and altitude. RAAN can be also estimated by the given longitude of the launch site and the location of λ Piscium, assuming a quick and straight burn-out phase. As a summary of these values:

Parameter Value

Orbital Period 5258.7s

Inclination 96.2 deg

RAAN -146.9 deg

Validation of these results was performed using an STK simulation and it was, for example, confirmed that the satellite orbits the earth about 17 times per sidereal day

Final Results/FeasibilityGiven the calculations, the 100lb payload can be launched into a sun synchronous orbit, with a bit of fuel to spare.

-The mission is feasible, the launch system was designed with extra possible losses in mind, therefore it produces a burnout speed that is more than enough (from the ideal rocket equation)

-Both a numerical simulation and STK verify a successful mission

Summary/Conclusion • Orbital parameters were validated and the requirements

derived• Meaningful rocket characteristics were derived based on the

requirements:• 3 Stages• Fuel: RP-1 & LOX (2.56 O/F ratio) • Material: Titanium (grade 5)• Maximum altitude:165.89km• Range: 35.16km• 3 fuel tanks, with a total volume of 8 m^3• Isp=322s• DV=3000m/s per stage

• The final design fulfills the mission requirements