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The Bloodhound SSC Land Speed Record Challenge – An Independent Appraisal

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The Bloodhound SSC Land Speed Record Challenge– An Independent Appraisal

- Achieve and possibly break the 1000 MPH speed mark for a land vehicle.
- Stimulate the interest for mathematical and physical subjects (STEM).
- Science
- Technology
- Engineering
- Mathematics
- Encourage young people into engineering.
- Generate an iconic project based upon extreme research and technologies, stretch the state-of-the-art envelope and spread the knowledge as widely as possible.
- Allow the general student population, throughout the world, to participate in an open-access scheme.
- Generate a substantial and lasting exposure for the project's sponsors.

What is sought:

- 1000 MPH equals 1.314 the speed of sound or 447 meters per second.
- Approximately 100 thousand horsepower are required to overcome air drag.
- The combined action of an advanced jet fighter engine and a hybrid rocket may provide this enormous power.

How to fulfill these goals:

The complete multidisciplinary team is made up of 49 persons directly in charge of materials, mechanics, aerodynamics, combustibles, integration, stability, control systems, communication systems, assembly, logistics and so on.

Who is doing the job?:

1898: 39.240 MPHJeantaud, electric, Gaston de Chasseloup, France.

1997: 763.002 MPHThrust SSC, turbofanAndy Green, UK.

Green Line: Speed of sound, 761.222 MPH @ 15 °C.

The large step in 1965 belies an important technological change: usage of jet engines for thrust.

A source of fascination

Speed of sound is temperature-dependent:

Air isentropic constant (diatomic)

Subsonic

At rest

Gas constant for air

Thermodynamic temperature

Therefore:

Supersonic

Transonic

- Bristol Bloodhound
- British designed surfaceair missile with an 85 km range.
- Capable of achieving 2.7 times the speed of sound.
- Thrust provided by two ramjets and four solid fuel rockets.
- Accelerates to the speed of sound in a mere 2.5 seconds.
- In service from 1958 until 1991.
- First design by Mr. Ron Ayers, now in charge of the Bloodhound SSC aerodynamical development.

WhyBloodhound ?

- Within two minutes the Bloodhound SSC:
- Accelerates from standstill, up to 1000 MPH and back to rest.
- Traverses clocked mile in 3.6 seconds.
- Acceleration subjects pilot to twice the force of gravity.
- Deceleration force is 3.5 × g.
- Distance travelled is almost 12 miles.
- Fuel consumption is almost 250 kg; propellants expenditure is 1144 kg.
- One hour allowed for turn-around to attempt return run.

A typical sequence

blue: speedred: accelerationgreen: clocked mile

- Hakskeen Pan, at the NW corner of South Africa, close to the Namibian border, at a 794 meter altitude.
- A extremely flat and wide stretch of desert with a very hard, compact surface.

Where it may be driven at 1000 MPH

- The speed record for low flying aircraft amounts to 988 MPH. Not even the Lockheed StarfighterF-104, one of the best-ever advanced fighter jets, has done it to 1000 MPH at low altitude.
- From 763.002 to 1000 MPH there is a 31% step, an extremely difficult feat where gains usually come very slowly and painfully in exchange for enormous investments.
- Some other stuff they must watch out for:
- Keep the car from taking-off like an airplane
- Ensure it follows a straight path
- Keep it from breaking into pieces. Air acts like a solid wall at 1000 MPH.

Are they serious about 1000 MPH?

- Built out of solid aluminum, at 149 kg each.
- At 1050 MPH their rotational speed exceeds 10000 RPM.
- For these conditions, the centrifugal force is around 51000 times stronger than gravity.
- Computer-based finite-element software was tapped for their design.
- Equipped with peripheral grooves which "bite" into the terrain to aid steering over a straight path.

No rubber tire will take such monumental stress

- Static thrust = 60 kN, dry; 90 kN, w/ afterburner(sea-level, 15 °C).
- Mass flow = 76 kg / s(1.225 kg / m3 air density at sea-level).
- Volumetric flow = 62 m3 / s(can displace all air in mid-size room in 0.62 s).
- Fuel consumption = 0.25 kg / s, idle; 4.32 kg / s, full afterburner.
- Total fuel expenditure = 250 kg(for 60 second working cycle).

Same type that powers Eurofighter Typhoon

- 111 kN average thrust.
- Equivalent power output = 77 500 HP.
- Burn time = 20.1 s.
- HTPB Hydroxyl-terminated polybutadiene(rubber), fuel = 181 kg.

Especifically designed for this job

- HTP High-test peroxide,(H2O2) oxidizer = 963 kg.
- Total propellant mass = 1144 kg.
- Total impulse = 2230 kN×s.

HTP

- 800 BHP @ 18 000 RPM.
- Drives the HTP oxidizer pump at 7.58 MPa pressure with 47.6 kg / s mass flow rate.
- Powers the 24-volt generator for the vehicle's electrical system.
- Delivers hydraulic pressure for air-brakes and friction brakes.

Same engine as used for Williams F-1 racing

Air drag retarding force exerted over a body moving through a fluid is;(u is speed in m / s):

CD A is speed-dependent drag area in m2; approximated by curve fitting:

r is air density in kg / m3, influenced by altitude and pressure;whereas p0 = 101 325 Pa is the reference atmospheric pressure:

x is the altitude-dependent coefficient (standard atmosphere); z is altitude in meters; T is thermodynamic temperature in kelvin

Substitution of all factors into air-drag equation leads to the final expression for this retarding effect:

As shown in graph, for speeds around 1000 MPH the drag force acting against the vehicle lies on the 17-ton range. This, together with the 447 m / s metric equivalence of speed yields a power requirement of 101 913 horsepower:

Taking into account the 90 kN static thrust FS0 provided by the EJ200 turbofan for standard sea-level conditions, as well as the fact that this unit is called upon to perform under non-standard, non-static conditions, the following expression applies to the net thrust:

Whereas T0 = 288.15 kelvin is the standard reference temperatureand = 76 kg / s is the reference mass flow rate at sea-level.

If the appropiate numerical values are substituted, an equation for the net thrust, as provided by the EJ200, results:

In addition, considering that the 111 kN average thrust from the Falcon hybrid rocket is not affected sensibly by the environmental conditions, a final expression for the total available thrust is found:

FN

Fd

FR

Frr

The equilibrium conditions applicable to the maximum (constant) speed regime may be described by the following equation;(the Frr rolling resistance component being neglected)

By substituting the numerical expressions formerly derived, a higher-order algebraic equation (ordered in descending powers of the speed u) results:

Numerical coefficients and parameters programmed into memory registers:

Next, according to the stored values, the equation editor is used to input the expression:

Finally, upon invoking the equation solver and following the prompts, the solution arises:

Multiplying the displayed solution (given in m / s) to get km / h and converting to MPH:

This particular solution applies to a 794 meter altitude and a 30 °C (303.15 K) ambient temperature.

Repeating the process for assorted altitude and temperature values, the following table and graph may be built from the resulting data set:

Thank you