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ESA Document - Emits - ESA

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s<br />

HMM<br />

Assessment Study<br />

Report: CDF-20(A)<br />

February 2004<br />

page 357 of 422<br />

Hv = The maximum residual horizontal velocity at contact with the surface.<br />

• Max. Horizontal Velocity 1 m/s<br />

Additional Data:<br />

• Lander Mass = 42000 Kg.<br />

• Vehicle CoG Height about 6 m.<br />

• Mars Gravity constant = 3.8 m/s2.<br />

Additional assumptions:<br />

• Assume deceleration time the same for both velocity components= 0.5 secs.<br />

• A margin or 2.5° added to α.<br />

• This approach excludes any Lander attitude errors or surface terrain effects.<br />

• Damping in the leg system is not taken in to account other than applying the deceleration<br />

time.<br />

Stability or no toppling is assumed when α is chosen such that FMV=FMH i.e induced moments<br />

are equal.<br />

The following remarks can be made regarding this analysis approach:<br />

• The problem is handled as a quasi-static problem.<br />

• As formulated above, the analysis excludes the changing velocity vector due to the<br />

rotation over or about the foot or feet.<br />

• Any induced rotation will be experienced as ‘damping’ for the toppling motion due to the<br />

Gravity vector- this can be treated as a (small) ‘margin’<br />

The analysis has been performed according to the following steps:<br />

1. Calculate the velocity at surface impact at minimum and maximum residual velocities<br />

using v2= u2+ 2.a.s where ‘u’ is the residual velocity, ‘’is the Martian gravitational<br />

constant and ‘s’ is the height at which the engine thrust is cut.<br />

2. Calculate the Vertical Force component (Fv) due to the deceleration [mass * (Fv/0.5<br />

secs)].<br />

3. Calculate the Horizontal Force component (Fh) for 3 horizontal velocities (Hv = 0.5 m/s,<br />

1 m/s & 1.5 m/s) [mass * (Hv/0.5)].<br />

4. Calculate the angle α where Fmv = Fmh [α = atan(Hv/Fh) + 2.5° margin] for minimum<br />

and maximum vertical velocities.<br />

5. Calculate the minimum footprint area required based upon the estimated CoG height.<br />

6. Compare the required minimum footprint dimension against the available envelope<br />

dimension.<br />

The above model has been reshown in an ‘excel’ spreadsheet. The following graph represents the<br />

output from the analysis.

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