The Bloodhound SSC Land Speed Record Challenge – An Independent Appraisal. Main drives. 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
What is sought:
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)
Gas constant for air
A typical sequence
blue: speedred: accelerationgreen: clocked mile
Where it may be driven at 1000 MPH
Are they serious about 1000 MPH?
No rubber tire will take such monumental stress
Same type that powers Eurofighter Typhoon
Especifically designed for this job
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:
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: