This is straight from Evans, a good starting place for
understanding the mathematics of flight.

Evans also developed a straight forward design spreadsheet
that brings it all together as a performance estimate.

It takes all the following and puts it in columns by airspeed
from 40 to 200 mph. That is usually in range of what people
design. But here, with only 13 hp, you would want to expand
the low speed end of the table.

Often, low and slow machines are dominated by parasitic drag.
Open structure, lots of struts and wires. Guess high and then
double it!

That has implications on performance.
Like cruise speed and stall speed at the same place on the clock?
Also very little excess power for climb.
(Lift HAS to be higher than weigh to climb

When you have some idea of the drag estimate, the performance
numbers can be estimated.

Once the airplane is completed and flying one can actually measure
all the parameters that were initially wild guesses.


The Equations

Basic descriptive equations - Equ 1..14
Drag in all it's many forms - Equ 15..19
Performance estimate - Equ 20..28

Equasions are numbered for reference.
Variable definitions at end of the page


CHAPTER 1 AERODYNAMICS
-----------------------
GENERAL
-------

(1) Q = .00256 V^2

(2) Gross Weight Estimate:

Gross Wt.(1 place) = Payload /.35

Gross Wt.(2 place) = Payload /.40

(Payload = Persons * Baggage + Fuel)


(3) Reynolds No. (RN) = 778 * c * V

(4) V Stall (Vs) = 20 * sqrt((W/S)/CLmax)

(5) Wing Area (S) = W / ( Q * CLmax)

(6) Wing Area (S) = (391 W) /(V^2 * CLmax)

(7) CL = W / (S * Q)

(8) CL = 391 * W / (S * V^2)

(9) Lift (L) = CL * S * Q

(10) Lift (L) = (S * CL * V^2) / 391

(11) Span (b) = S /C (both the same - inches or feet)

(12) Chord (C) = S/b

(13) Wing Loading = W / S

(14) Aspect Ratio (AR) = b/C or b^2/S


DRAG
----

WETTED AREA DETERMINATION (Sw )
-------------------------


(If the airplane was totally immersed in water, all surfaces would be
wetted.)

(a) Add exposed wing and tail areas and multiply by 2.06 for curved area
of top and

bottom surfaces.

(b) Divide fuselage length into a number of sections, Multiply perimeter
of each cress

section by its longitudinal width. Add rear surfaces.

(c) Sum up all surface areas = S


COEFFICIENT OF FRICTION (Cf )

-----------------------
Super clean Sailplane Cf =.003
Clean Q2, Dragonfly .005
Enclosed Basic Trainer, Mono .009
Open Biplane, Exp. Radial .014


(15) Parasite Drag (Dp) = Cf Sw q

(16) Parasite Drag (Dp) = (D/q) x q ???

(17) Coef. Induced Drag (Cdi) = CL^2 /(Pi * AR)

(18) Induced Drag (Di) = Cdi S q

(19) Total Drag (DT)= Di +Dp


Ercoupe = 4.4
Cherokee 180 = 3.9
Varieze = 2.1
Lancair 200 = 1.6
Q2 = 1.3
Dragonfly = 1.3



PERFORMANCE
-----------

(20) Prop Eff. (n) = .85
(less for shorter props, more for longer)
(at 3000 RPM n .5)!!!

Prop n = .85/(1+( DT /Q * Prop Diameter^2)

(21) Thrust HP Req. = D * V /375

(22) Max THP (Tm)= n(BHP)

(23) Cruise THP(Tcr) = .75 (.90 for VW)

(24) Climb THP (Tcl) = .90 (.95 for VW)

(25) Level Flit THP Req (TL) = .00267 * (DV/n)

(26) Excess THP (Te) = Tcl - TL

(27) Rate Climb (RC) = (Te * 33,000) /W

(28) THP req. climb = (RC * W) / 33000



WHE
V = Velocity in MPH
Persons = 170 pounds
Baggage = 4 pounds each
Fuel = 6 pounds / gallon
C = chord in inches
W = Weight in pounds (usually Gross weight)
L = Lift in pounds
D = Drag in pounds
S = surface in Sq Ft
rc = rate of climb in ft/Min
n = effeceincy
pd' = prop diameter in feet

CLmax:
Fabric = 1.2
Metal = 1.3
Composite = 1.35

*