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
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