Iteration 2: Weight and Airfoil#

from unyt import km, m, mm, g, kg, hr, s, degree, radian
import numpy as np
from math import pi as π

ρ = 1.225*kg/m**3 # air density
μinf = 1.81e-5*kg/(m*s) # viscosity of air

Goals:

  • Decrease aspect ratio

Initial Design#

b = 2850*mm # wingspan
c = 230*mm # chord

S = b*c # wing area
AR = b**2/S

AR

unyt_quantity(12.39130435, '(dimensionless)')

Better, although I may have overdone it

Weight Estimate#

Weight taken from Freecad model > Parts spreadsheet.
Freecad model not saved :(

W = 3700*g # weight

Airfoil Selection#

See also: https://youtu.be/kAXN3MlQxxc

V = 45*km/hr # cruise speed

Randomly selected, see https://rcmodelhub.com/how-fast-do-rc-planes-go/#0-typical-speeds-of-popular-rc-planes-

CL = (2*W)/(ρ*V**2*S)
CL.to('s**2/m')

unyt_quantity(0.05897975, 's**2/m')

Re = (ρ*V*c)/μinf
round(Re.to_value(), -3)

195000.0

As per: http://airfoiltools.com/airfoil/details?airfoil=clarky-il
Clark Y chosen because:

  • No need for inverted flight

  • Long term goal is efficiency

  • Relatively easy foam manufacturing

clarky-cl-v-alpha

From bottom left up: Blue = 50,000 Orange = 100,000 Green = 200,000

# rough estimations
α0 = -3.75*degree
Clα = 1.05
e = 0.8

CLα = Clα/(1+(Clα/(π*e*AR)))
CLα

unyt_quantity(1.01575315, '(dimensionless)')

CL_unitless = CL.to_value('s**2/m')
CL_unitless

0.05897974750540949

α = α0+((CL_unitless/CLα)*radian)
α

unyt_quantity(-0.42311827, 'degree')

clarky-cl-cd-v-alpha

Notes#

I previously used a lift curve slope (Clα) of 0.083 (instead of 1.05), because I misread the Cl v Alpha graph. This resulted in an α of 0.667 or 38°. My conclusion was:

Oops, angle of attack for cruise is uncomfortably close to aerodynamic stall. It should ideally be about 5° (see Cl/Cd v Alpha below).

We can increase CL by:

  • Increasing air speed

  • Increasing wing area

Decreasing weight is not a possibility

As α is now well below 10° (the point of aerodynamic stall for the Clark Y), this is not really applicable anymore. In fact, I have since actually changed my weight estimate downward because I had a feeling I was overestimating the wing weight (3744 -> 2340).

Since the cruise angle of attack is now actually on the low side, I’ll lower the airspeed in the next iteration. This will hopefully get us closer to 5°. Not exactly 5, but at least something higher than 0.