In simple swept-wing flow theory, the freestream Mach component normal to a swept reference line is represented by M cos(Lambda). This calculator compares that scalar projection for two entered angles.
Variable-sweep Wing Pivot Interactive Calculator
Enter flight Mach and two sweep angles. Results are ideal M cos(Lambda) projections and arithmetic comparisons—not drag-rise predictions, aerodynamic performance or pivot design.
Equation Used
- Mach is treated as a scalar freestream magnitude.
- Each entered angle is used directly in the ideal cosine projection.
- The two cases share the same entered flight Mach.
- Finite-wing flow, thickness, lift, angle of attack, shocks, drag, aeroelasticity, stability, structure, pivot loads and safety are omitted.
Ideal Simple-Sweep Vector Projection
NACA and NASA swept-wing references describe the freestream component normal to a swept reference line using cosine relations, while also noting that real finite wings do not necessarily obtain the full benefit predicted by simple-sweep theory. This calculator evaluates only that scalar projection.
What This Calculator Represents
The tool multiplies entered Mach by the cosine of each entered angle, compares the two projected values and subtracts case A from 1.
Ideal Projection Calculations
MnB=M cos(LambdaB)
relative difference=100(1-MnA/MnB)
signed difference from 1=1-MnA
These are scalar vector-projection results only.
Worked Idealized Example
At M=2.34, angle A=68 degrees gives MnA about 0.88, while angle B=20 degrees gives MnB about 2.20. The relative difference is about 60.1% and the signed difference 1-MnA is about 0.12.
Model Boundary
- Calculated: two M cos(Lambda) scalar projections, their relative arithmetic difference and one signed difference from 1.
- Illustrated: two ideal vector-projection directions at the entered angles.
- Not calculated: drag rise, shocks, lift, buffet, stability, performance, finite-wing flow, aeroelasticity, structure, pivot loads, actuation, fatigue or safety.
Frequently Asked Questions
Does Mn below 1 prove shock-free flow?
No.
Is the reported margin an aerodynamic safety margin?
No; it is only 1-MnA.
Does this predict drag-divergence Mach?
No.
Does it include finite-wing effects?
No.
Does it calculate pivot loads?
No.
Can it establish an operating envelope?
No.
References
- NACA RM A50I27: normal Mach and freestream Mach are related through the cosine of sweep in simple swept-wing flow theory.
- NASA TN D-7931: normal-component Mach definitions and limits of simple-sweep cosine benefit for real swept wings.
- NACA swept-wing tunnel investigation: measured changes were somewhat less than a simple 1/cos(sweep) factor.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
