Aerospace engineering cheat sheet

Momentum

Linear momentum combines mass and velocity. Force relates to its rate of change for a defined system.

p = mv

Dynamic pressure

Dynamic pressure in a basic flow model depends on fluid density and speed squared.

q = ½ρv²

Specific impulse

Specific impulse compares thrust with propellant mass flow multiplied by standard gravity. It is a propulsion performance measure, not a direct measure of thrust.

Isp = thrust ÷ propellant weight-flow rate

Circular orbit model

For an ideal circular orbit around a dominant point or spherical mass, gravity supplies centripetal acceleration.

v = √(GM/r), where r is measured from the centre.

Reference frames

Position, velocity and force components must be expressed in a consistent frame. A change of frame can change coordinate values without changing the physical event.

Distinguish Earth-fixed coordinates from a vehicle’s body axes.

Drag models

A common drag model is D = ½ρV²CD A. The reference area, coefficient and flow conditions must be specified; CD is not a universal constant for an object.

Shape, orientation and flow regime influence the coefficient.

Mass ratio and ideal velocity change

The ideal rocket equation relates velocity change to effective exhaust velocity and mass ratio: Δv = ve ln(m₀/mf). It excludes losses such as gravity and aerodynamic drag.

A larger propellant fraction changes mass ratio; it is not the same thing as a larger exhaust velocity.

Orbital motion

In a simplified circular two-body orbit, gravity supplies centripetal acceleration. Orbital speed depends on distance from the centre of the attracting body.

v = √(GM/r), where r is centre-to-centre distance, not altitude above the surface.

Worked example: model drag

For ρ = 1.2 kg/m³, V = 20 m/s, CD = 0.1 and A = 2 m², D = ½ × 1.2 × 20² × 0.1 × 2 = 48 N.

At unchanged conditions and coefficient, halving V reduces this model drag to 12 N.

Common mistake: a vacuum has no gravity

Removing air eliminates aerodynamic effects, not gravity. An orbiting spacecraft is in continuous free fall; apparent weightlessness is not evidence that gravitational attraction is zero.

Separate gravitational force from a supporting contact force when drawing a free-body diagram.

Check your understanding

In v = √(GM/r), is r the spacecraft’s altitude?

No. It is the distance from the attracting body’s centre in this simplified model.

Curriculum connections

Sources