HP 32SII: Glide Slope Calculations (and Memory Management)
Note: These programs should work on the Swiss Micros DM32.
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:
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.
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/Portals/7/Mathematics%20of%20Flight%20Glide%20Slope%20II.pdf
Eddie
All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
