(32SII) Glide Slope Calculations

[Eddie W. Shore]

Introduction

The following program calculates the forces and angle for a flight of a glider, an aircraft without a engine:

* Weight
* Lift Force
* Drag Force

SI units are used.

With inputs glide distance (G), height (H), and mass (M):

Angle: A = arcsin(H ÷ G)

Weight: W = M × 9.80665

Lift: L = W × sin A

Drag: D = W × cos A

The program uses the polar-to-rectangular conversion to calculate lift and drag.


HP 32SII Programs: Glide Slope Calculations

Code 1:

Code:

G01  LBL G
G02  DEG
G03  INPUT G
G04  INPUT H
G05  INPUT M
G06  R↓
G07  x<>y
G08  ÷
G09  ASIN
G10  STO A
G11  VIEW A
G12  R↑
G13  9.80665
G14  ×
G15  STO W
G16  VIEW W
G17  θ,r→y,x
G18  STO L
G19  VIEW L
G20  x<>y
G21  STO D
G22  VIEW D
G23  RTN

Bytes: 42.5
Checksum: 4717

Notes:

* This version has prompts and view commands to guide the user. We don't have to preload registers as the INPUT commands guide us.

* All inputs and outputs are stored to variables. 7 variables are used, which will require 56 bytes. On the HP 32SII, each variable that contains non-zero values takes 8 bytes of memory. If you want to make the variables local, insert a CLVARS command for G23 and line G24 becomes RTN.

Variables:

Input:

G = Glide Distance. The distance that glider climbs to it's peak. Think of the hypotenuse of a right triangle. Distance is in meters.

H = Height. The height that the glider reaches. Distance is in meters.

M = Mass. Mass of the glider in kilograms.

Output:

A = Angle. Angle of the of glider's flight in degrees.

W = Weight. Weight of the glider, which is Newtons.

L = Lift force of the glider, in Newtons.

D = Drag force of the glider, in Newtons.

Code 2:

Code 2 is a shorter code which does not store anything into variables. The program starts with G (glide distance), H (height), and M (mass) on the stack.

Code:

L01   LBL L
L02   DEG
L03   R↓
L04   x<>y
L05   ÷
L06   ASIN
L07   STOP  (display A)
L08   R↑
L09   9.80665
L10   ×
L11   STOP  (display W)
L12   θ,r→y,x
L13   RTN    (L is on the x stack, D is on the y stack)

Bytes: 27.5 bytes
Checksum: 6446


Examples

Example 1:
Glider distance: G = 178 m
Height: H = 23 m
Mass of the glider: M = 55 kg

Output:
Angle: A ≈ 7.4241°
Weight: W ≈ 539.3658 N
Lift: L ≈ 534.8441 N
Drag: D ≈ 69.6933 N


Example 2:
Glider distance: G = 200 m
Height: H = 30 m
Mass of the glider: M = 39 kg

Output:
Angle: A ≈ 8.6269°
Weight: W ≈ 382.4594 N
Lift: L ≈ 378.1322 N
Drag: D ≈ 57.3689 N


Source

National Museum of the United States Air Force. "Mathematics of Flight: Glide Slope II" September 2020. Retrieved August 2023.
https://www.nationalmuseum.af.mil/Portal...e%20II.pdf

What do you prefer: (1) programs with prompts and stores the results or (2) programs that uses the stack and saves as much memory as possible?

[knife31]

Wonder if this would work for a 747 with total engine failure.