Combined Plane Change Savings
Compare a combined speed/plane-change impulse with speed change plus a plane change at the lower endpoint speed; geometry must be co-located.
Description
Combining a speed change and plane rotation at one point can reduce impulse compared with doing two separate vector changes.
Combining a speed change and plane rotation at one point can reduce impulse compared with doing two separate vector changes. The comparison depends on the explicitly chosen separate-burn convention.1
Compare a combined speed/plane-change impulse with speed change plus a plane change at the lower endpoint speed; geometry must be co-located.
When to use Combined Plane Change Savings
Use this tool to compare a combined speed/plane-change impulse with speed change plus a plane change at the lower endpoint speed; geometry must be co-located.
Prepare the orbital state or model parameters in one reference frame. Confirm compatible distance/time units and the stated angular and gravitational-parameter conventions.
How to use Combined Plane Change Savings and understand its results
- Prepare the orbital state or model parameters in one reference frame. Confirm compatible distance/time units and the stated angular and gravitational-parameter conventions.
- Enter incomingSpeed, outgoingSpeed, planeAngleDegrees using the field table and calculation rules, then run the tool.
- Read combinedDeltaV, separateDeltaV, savedDeltaV. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| incomingSpeed | Incoming speed | number | Required |
| outgoingSpeed | Outgoing speed | number | Required |
| planeAngleDegrees | Plane angle degrees | number | Required |
Enter nonnegative endpoint speeds in a common unit and plane angle 0–180 degrees. The tool calculates combined impulse by the cosine law and separate impulse using a plane change at the lower speed. Return both magnitudes and separate-minus-combined savings; zero plane angle reduces to the speed-change magnitude.
combined = sqrt(v1²+v2²−2v1v2 cosθ); separate = |v2−v1|+2 min(v1,v2)sin(θ/2) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| combinedDeltaV | Combined delta v | number |
| separateDeltaV | Separate delta v | number |
| savedDeltaV | Saved delta v | number |
{
"input": {
"incomingSpeed": 3,
"outgoingSpeed": 4,
"planeAngleDegrees": 90
},
"output": {
"combinedDeltaV": 5,
"separateDeltaV": 5.242640687119285,
"savedDeltaV": 0.24264068711928477
}
}Limitations and assumptions
Vectors are assumed co-located and geometrically achievable. This does not optimize a full transfer or handle different burn locations, finite maneuvers or propellant.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Pure Plane Change Impulse: Calculate an instantaneous pure plane rotation at constant speed; actual node availability is not inferred. For a complementary task, use Hohmann Transfer Budget: Compute both coplanar Hohmann burn magnitudes, total impulse, and half-period coast time for circular endpoints.
References
-
Combined Plane Change Savings — tool.io
Similar or alternative tools
- Pure Plane Change Impulse
Calculate an instantaneous pure plane rotation at constant speed; actual node availability is not inferred.
- Hohmann Transfer Budget
Compute both coplanar Hohmann burn magnitudes, total impulse, and half-period coast time for circular endpoints.