Exponential Entry Peak Deceleration

Evaluate the constant-flight-path, drag-only Allen–Eggers exponential-atmosphere peak-deceleration approximation; lift and changing entry angle are neglected.

Description

A drag-only entry through an exponential atmosphere admits an approximate peak deceleration under a constant flight-path angle.

A drag-only entry through an exponential atmosphere admits an approximate peak deceleration under a constant flight-path angle. The scale height and entry speed describe this idealized environment.^[1]

Evaluate the constant-flight-path, drag-only Allen–Eggers exponential-atmosphere peak-deceleration approximation; lift and changing entry angle are neglected.

When to use Exponential Entry Peak Deceleration

Use this tool to evaluate the constant-flight-path, drag-only Allen–Eggers exponential-atmosphere peak-deceleration approximation; lift and changing entry angle are neglected.

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 Exponential Entry Peak Deceleration 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 entryMetersPerSecond, downwardAngleDegrees, scaleHeightMeters, referenceGravityMetersPerSecondSquared using the field table and calculation rules, then run the tool.
Read peakMetersPerSecondSquared, peakGravityLoads. 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
entryMetersPerSecond	Entry meters per second	number	Required
downwardAngleDegrees	Downward angle degrees	number	Required
scaleHeightMeters	Scale height meters	number	Required
referenceGravityMetersPerSecondSquared	Reference gravity meters per second squared	number	Required

Enter positive speed in m/s, scale height in m and reference gravity in m/s², with downward angle magnitude strictly above 0 and at most 90 degrees. Return peak deceleration magnitude in m/s² and its ratio to the supplied gravity.

peakAcceleration = entrySpeed² sin(downwardAngle)/(2e × scaleHeight)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
peakMetersPerSecondSquared	Peak meters per second squared	number
peakGravityLoads	Peak gravity loads	number

json

{
  "input": {
    "entryMetersPerSecond": 1,
    "downwardAngleDegrees": 30,
    "scaleHeightMeters": 1,
    "referenceGravityMetersPerSecondSquared": 1
  },
  "output": {
    "peakMetersPerSecondSquared": 0.09196986029286057,
    "peakGravityLoads": 0.09196986029286057
  }
}

Limitations and assumptions

This Allen–Eggers approximation omits lift, changing angle, detailed atmosphere, heating and trajectory integration. It is not an entry or occupant-load certification.

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 Entry Ballistic Coefficient: Compute the mass-to-drag-area ballistic coefficient from supplied aerodynamic reference quantities. For a complementary task, use Aerocapture Corridor Margin: Audit a predicted entry-angle uncertainty band against a supplied aerocapture corridor; no atmosphere-specific corridor is embedded.

References

Exponential Entry Peak Deceleration — tool.io

Similar or alternative tools

Entry Ballistic Coefficient
Compute the mass-to-drag-area ballistic coefficient from supplied aerodynamic reference quantities.
Aerocapture Corridor Margin
Audit a predicted entry-angle uncertainty band against a supplied aerocapture corridor; no atmosphere-specific corridor is embedded.