Bike1 - DM15c Program (Ebike maximum speed - Bike power for a given speed - Bike development)

Description

J E Patterson - jepspectro.com - 20231119

This program works with the DM15C series of calculators by SwissMicros. The extended memory firmware should be installed. The hp15c Simulator by Torsten Manz can be used as well if the DM15C preferences are set to 229 registers. The programs are self-contained so they can be extracted as separate programs.

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EbikeMax - Ebike maximum speed from given hub motor rpm - J E Patterson - jepspectro.com - version 20160210

EbikeMax starts at line 1 and ends at line 34

This program calculates the maximum speed of a hub motor Ebike at 36 volts and 42 volts, given the specified motor rpm and the bike wheel size.

Enter motor rpm
ENTER
Enter wheel size in inches or mm - the program works out if the units are inches or mm from the magnitude
GSB A

The maximum speed at 36 volts is displayed.
Press R/S.
The maximum speed at 42 volts is displayed.

speed km/h = 4.79E-3 x motor rpm x wheel size in inches at 42 volts
25.4 x pi x 60 / E^6 = 4.79E-3.

Speed is proportional to the battery voltage and the wheel diameter.
Speed is also limited by hills and wind.
For a 20 inch wheel the bike speed in km/h at 42 volts is approximately motor rpm/10.

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Bike Power - J E Patterson - jepspectro.com - version 20160119

Bike Power starts at line 35 and ends at line 114

This program calculates the power Pw required to allow a bike plus rider of weight W to attain a given bike speed Vr on a grade G and also into a given head wind.

Enter total weight W (kg),
STO 1. This weight W includes the bike plus rider.

Enter the grade G (%) of the road,
STO 2. For a flat road enter 0, STO 2

Enter V (km/h)
GSB B

The required power P (watts) to reach a bike speed V (km/h) is displayed.

Enter a head wind speed in km/h. This is an optional step..
Press R/S

The power Pw required to maintain the same speed into the head wind is displayed.

Stored results:
R4 = Power required to overcome air drag resistance, Pd
R6 = Power required to overcome rolling resistance, Pr
R7 = Power required to overcome % grade G, Ps
R8 = The total required power, P = (Pd + Pr + Ps) * 1.0309
R9 = The power required into a head wind, Pw = (R4 * (Va/Vr)^2 + R6 + R7) * 1.0309

There are constants in the program:
1.0309 = 1/(1 - 3/100) compensates for a 3% drive-train loss.
0.2778 = 1000/3600 converts km/h to m/s
0.2626 = 0.5 x (Air Density (1.226) * Drag coefficient Cd (0.63) * Frontal area (0.68))
Reduce this constant in proportion for a more streamlined setup

0.0490 = g (9.8067) * Coefficient of rolling resistance Crr (0.005)
9.8067 = g acceleration due to gravity (m/s²)

Equations:
Pd = Vr * 0.5 * rho * Va^2 * Cd * A
Pr = Vr * m * g * cos(arctan(s)) * Crr
Ps = Vr * m * g * sin(arctan(s))
P = (Pd + Pr + Ps) * 1.0309

Va = Vr + head-wind speed (m/s)
Vr = Va in still air.
Pw = (R4 * (Va/Vr)² + R6 + R7) * 1.0309

Terms:
rho = air density = 1.226 kg/m³
Cd = drag coefficient 0.63
A = frontal area 0.68 m² - upright riding style
m = mass kg = W
g = acceleration due to gravity = 9.8607 m/s²
Crr = coefficient rolling resistance 0.005
s = slope = G/100
Vr = bike road speed (m/s)
Va = bike air speed (m/s)

References:
https://en.wikipedia.org/wiki/Bicycle_performance
http://www.bikecalculator.com

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Bike Development - J E Patterson - jepspectro.com - version 20160210

Bike Development starts at line 115 and finishes at line 159

Gear-inches, Metres-development and Gain-ratio are calculated.

Enter wheel diameter in inches or mm - the program works out if the units are inches or mm from the magnitude
Enter front sprocket teeth number
Enter rear sprocket teeth number

GSB C returns Gear-Inches
R/S returns Metres-Development
R/S returns Gain-Ratio for a 170 mm crank arm

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Bike Speed

Bike Speed starts at line 160 and ends at line 167

Run Bike Development first
Enter cadence in RPM
GSB D
The bike speed in km/h is returned

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Program Resources

Labels

Name	Description
A	Ebike maximum speed from hub motor rpm
B	Power required for a given bike speed
C	Bike development
D	Bike speed

Storage Registers

Name	Description	Name	Description
1	Speed 36V,W,GI	6	Pr, Gain Ratio
2	Speed 42V,G,25.4	7	Ps
3	V m/s, 25.4,front/rearT	8	Pt
4	Pd, Wheel size in inches,Gear Inches	9	Pw
5	ArcTan(G/100), Metres development

Program

Line	Display	Key Sequence	Line	Display	Key Sequence	Line	Display	Key Sequence
000			056	43 25	g TAN-¹	112	20	×
001	42,21,11	f LBL A	057	44 5	STO 5	113	44 9	STO 9
002	2	2	058	24	COS	114	43 32	g RTN
003	5	5	059	48	.	115	42,21,13	f LBL C
004	48	.	060	0	0	116	10	÷
005	4	4	061	4	4	117	44 3	STO 3
006	44 3	STO 3	062	9	9	118	20	×
007	33	R⬇	063	0	0	119	44 1	STO 1
008	2	2	064	20	×	120	2	2
009	0	0	065	45,20, 1	RCL × 1	121	5	5
010	0	0	066	45,20, 3	RCL × 3	122	48	.
011	34	x↔y	067	44 6	STO 6	123	4	4
012	43,30, 7	g TEST x>y	068	45 5	RCL 5	124	44 2	STO 2
013	45,10, 3	RCL ÷ 3	069	23	SIN	125	2	2
014	44 4	STO 4	070	45,20, 1	RCL × 1	126	0	0
015	33	R⬇	071	45,20, 3	RCL × 3	127	0	0
016	33	R⬇	072	9	9	128	45 1	RCL 1
017	4	4	073	48	.	129	45 3	RCL 3
018	48	.	074	8	8	130	10	÷
019	7	7	075	0	0	131	43,30, 7	g TEST x>y
020	9	9	076	6	6	132	45,10, 2	RCL ÷ 2
021	26	EEX	077	7	7	133	45 3	RCL 3
022	16	CHS	078	20	×	134	20	×
023	3	3	079	44 7	STO 7	135	44 4	STO 4
024	45,20, 4	RCL × 4	080	45 4	RCL 4	136	45 2	RCL 2
025	20	×	081	45,40, 6	RCL + 6	137	20	×
026	44 1	STO 1	082	45,40, 7	RCL + 7	138	44 1	STO 1
027	31	R/S	083	1	1	139	45 2	RCL 2
028	48	.	084	48	.	140	10	÷
029	8	8	085	0	0	141	45 1	RCL 1
030	5	5	086	3	3	142	43 26	g π
031	7	7	087	0	0	143	20	×
032	10	÷	088	9	9	144	26	EEX
033	44 2	STO 2	089	20	×	145	3	3
034	43 32	g RTN	090	44 8	STO 8	146	10	÷
035	42,21,12	f LBL B	091	31	R/S	147	44 5	STO 5
036	48	.	092	48	.	148	45 1	RCL 1
037	2	2	093	2	2	149	3	3
038	7	7	094	7	7	150	4	4
039	7	7	095	7	7	151	0	0
040	8	8	096	8	8	152	10	÷
041	20	×	097	20	×	153	44 6	STO 6
042	44 3	STO 3	098	45 3	RCL 3	154	45 4	RCL 4
043	3	3	099	40	+	155	31	R/S
044	14	yˣ	100	45,10, 3	RCL ÷ 3	156	45 5	RCL 5
045	48	.	101	43 11	g x²	157	31	R/S
046	2	2	102	45 4	RCL 4	158	45 6	RCL 6
047	6	6	103	20	×	159	43 32	g RTN
048	2	2	104	45,40, 6	RCL + 6	160	42,21,14	f LBL D
049	6	6	105	45,40, 7	RCL + 7	161	45 5	RCL 5
050	20	×	106	1	1	162	20	×
051	44 4	STO 4	107	48	.	163	48	.
052	45 2	RCL 2	108	0	0	164	0	0
053	26	EEX	109	3	3	165	6	6
054	2	2	110	0	0	166	20	×
055	10	÷	111	9	9	167	43 32	g RTN