Iteration 3: Propulsion#

from unyt import km, m, mm, inch, g, kg, hr, minute, s, degree, radian, volt
import numpy as np
from matplotlib import pyplot as plt
from math import pi as Ļ€
%matplotlib inline

rpm = minute**-1

Ļ = 1.225*kg/m**3 # air density
Ī¼inf = 1.81e-5*kg/(m*s) # viscosity of air

Goals:

  • Use more accurate weight estimate

  • Increase the AR a little (13 or something)

  • Decrease air speed

iteration_3-freecad-screenshot

Initial Design#

Increased wingspan from 2850 to 3050.

b = 3050*mm # wingspan
c = 230*mm # chord

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

AR

unyt_quantity(13.26086957, '(dimensionless)')

Weight Estimate#

Weight stimate lowered from 3700 to 2340.

W = 2340*g # weight

iteration_3-weight-tabulation

Airfoil Selection#

Cruise speed lowered from 45 to 30.

V = 30*km/hr # cruise speed

CL = (2*W)/(Ļ*V**2*S)

Re = (Ļ*V*c)/Ī¼inf
round(Re.to_value(), -3)

130000.0

clarky-cl-v-alpha

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

Ī±0 = -3.75*degree
ClĪ± = 1.05
e = 0.8

CLĪ± = ClĪ±/(1+(ClĪ±/(Ļ€*e*AR)))

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

Ī± = Ī±0+((CL_unitless/CLĪ±)*radian)
Ī±

unyt_quantity(0.66417137, 'degree')

clarky-cl-cd-v-alpha

The 0.1Ā° Ī± is better than -0.4, but still not great. I do think I may be understimating the weight and probably overestimating the wingā€™s 3D efficiency (currently 80%). Iā€™ll maybe come back to this.

CLmax = 1.4*s**2/m
Vstall = np.sqrt((2*W)/(Ļ*S*CLmax))
print(f"Cruise speed: {V.to('m/s'):.2f}, Stall speed: {Vstall:.2f}")

Cruise speed: 8.33 m/s, Stall speed: 1.97 m/s

Excellent! I feel like Iā€™m doing something wrong because these results are way too comfortable.

Wing Loading and Thrust to Weight Ratio#

WCL = W/(S**(3/2))
print(f"Wing loading: {WCL.to('kg/m**3'):.2f}")

Wing loading: 3.98 kg/m**3

Carlos Montalvoā€™s WCL ballpark table converted from oz/ft^3 to SI units.

Type of Aircraft

WCL (kg/m^3)

Gliders

under 4

Trainers

5-7

Sport Aerobatic

8-10

Racers

11-13

Scale

over 15

Ok so oz/ft^3 -> kg/m^3 is apparently nearly 1:1 for these values.

Anyway, our 3.98 is OK.

TtoW = 1.1

As per ā€˜Aircraft Flight Mechanicsā€™: T/W should be above 0.8 in all situations and above 1.2 to be safe with short runways. I did find other resources indicating a sub-.8 T/W is OK for gliders. However, it seems universally accepted that 1+ is necessary for 3D flight.

Because I do have future plans for high thrust takeoff with this design, I picked the above.

T = TtoW*W
print(f"{T.to('kg'):.2f}")

2.57 kg

Propulsion system#

To choose a propulsion system weā€™ll start by calculating the max speed we need to be able to reach.

Assuming we want cruise speed to be 65% throttle:

Vmax = V/0.65
print(f"Max speed: {Vmax.to('m/s'):.2f}")

Max speed: 12.82 m/s

We can then plot the minimum propeller Pitch Y v rpm. (assuming a Pitch Y efficiency of .8.)

pitchYe = 0.65
minPitchYPerMinute = (Vmax*(1/pitchYe)).to('inch/min')

minPitchY, maxPitchY = 2*inch, 17*inch
minRpm, maxRpm = minPitchYPerMinute/maxPitchY, minPitchYPerMinute/minPitchY
x = np.arange(minRpm, maxRpm, 100*rpm)
y = minPitchYPerMinute/x

fig = plt.figure()
ax = fig.add_axes([0, 0, 1, 1])
ax.grid(True)
ax.set_ylim([minPitchY, maxPitchY])
ax.set_xlim([minRpm, maxRpm])
ax.plot(x, y)
ax.set_title('Minimum Pitch Y v rpm')
ax.set_xlabel('rpm')
ax.set_ylabel('Minimum Pitch Y (inch)')

Text(0, 0.5, 'Minimum Pitch Y (inch)')
../../_images/iteration_3_propulsion_40_1.png

Or more usefully: the minimum Pitch Y versus the Kv rating for different LiPo cell compositions.

I also ran MotoCalc. You can find the results (and parameters I used) in iteration_3-motocalc-results.txt (and the project in iteration_3-motocalc-project.txt).

The top 4 recommendations are the following (also plotted below):

Kv

Cell Composition

Pitch Y

325

5S

7

480

4S

6

330

6S

7

250

5S

11

 
LiPo4SVoltage = 3.7*volt*4
LiPo5SVoltage = 3.7*volt*5
LiPo6SVoltage = 3.7*volt*6
LiPo7SVoltage = 3.7*volt*7

minKv, maxKv = minPitchYPerMinute/(maxPitchY*LiPo7SVoltage), minPitchYPerMinute/(minPitchY*LiPo7SVoltage)+200*(rpm/volt)
x = np.arange(minKv, maxKv, 5*(rpm/volt))
y4S = minPitchYPerMinute/(x*LiPo4SVoltage)
y5S = minPitchYPerMinute/(x*LiPo5SVoltage)
y6S = minPitchYPerMinute/(x*LiPo6SVoltage)
y7S = minPitchYPerMinute/(x*LiPo7SVoltage)

fig = plt.figure()
ax = fig.add_axes([0, 0, 1, 1])
ax.grid(True)
ax.set_ylim([minPitchY, maxPitchY])
ax.set_xlim([minKv, maxKv])
ax.plot(x, y4S, label = "4S")
ax.plot(x, y5S, label = "5S")
ax.plot(x, y6S, label = "6S")
ax.plot(x, y7S, label = "7S")
plt.plot([325], [7], marker='o', label = "325/5S/7")
plt.plot([480], [6], marker='o', label = "480/4S/6")
plt.plot([330], [7], marker='o', label = "330/6S/7")
plt.plot([250], [11], marker='o', label = "250/5S/11")
ax.set_title('Minimum Pitch Y v Kv')
ax.set_xlabel('Kv rating (rpm/volt)')
ax.set_ylabel('Minimum Pitch Y (inch)')
ax.legend()

<matplotlib.legend.Legend at 0x7f54e539a880>
../../_images/iteration_3_propulsion_43_1.png

In conculsion: Iā€™m aiming for a minimum 250/4S/12, 300/4S/8, 450/4S/6 but preferably 5 or 6S.

As for prop diameter: any combination of the above that gives me at least 2.6 kg of thrust.

Propulsion system component selection#

Possible combinations:

1. Turnigy G60 Brushless Outrunner 500kv (.60 Glow)#

https://hobbyking.com/en_us/turnigy-g60-brushless-outrunner-500kv-60-glow.html

Kv: 500
Max current: 65A
Price: ā‚¬57.41
Weight: 360g

5S LiPo (9250 rpm) + 13x8 prop: 869W 47A 2.85kg

Conclusion: OK

2. PROPDRIVE v2 5060 380KV Brushless Outrunner Motor#

https://hobbyking.com/en_us/propdrive-v2-5060-380kv-brushless-outrunner-motor.html

Kv: 380
Max current: 90A
Price: ā‚¬54.71
Weight: 438g

From reviews: 6S LiPo (8436 rpm) + 15x12 prop: 1110W 50A ???kg
thrust probably higher than the G60 (higher wattage)

Conclusion: OK

3. Turnigy G46 Brushless Outrunner 670kv (.46 Glow)#

https://hobbyking.com/en_us/propdrive-v2-5060-380kv-brushless-outrunner-motor.html

Kv: 670
Max current: 40A
Price: ā‚¬52.19
Weight: 303g

From reviews:
5S LiPo (12395 rpm) + 12x8 prop: 697W 43A 2.9kg
5S LiPo (12395 rpm) + 13x6 prop: 1000W 54A 3.1kg
I donā€™t quite get how current draw is exceeding the max hereā€¦

Conclusion: maybe OK, on the uncomfortable side with regards to the max current rating

4. PROPDRIVE v2 5050 580KV Brushless Outrunner Motor#

https://hobbyking.com/en_us/propdrive-v2-5050-580kv-brushless-outrunner-motor.html

Kv: 580
Max current: 90A
Price: ā‚¬49.58
Weight: 331g

From reviews:
6-7S? LiPo (14247 rpm) + 14x7 prop: 1298W 69A ???kg

Conclusion: OK

5. PROPDRIVE v2 4258 500KV Brushless Outrunner Motor#

https://hobbyking.com/en_us/propdrive-v2-4258-500kv-brushless-outrunner-motor.html

Kv: 500
Max current: 60A
Price: ā‚¬46.10
Weight: 300g

4S LiPo (Ā  7400 rpm) + 15x8 prop: Ā  Ā  421W 28.5A ???kg
5S LiPo (Ā  9250 rpm) + 15x8 prop: Ā  Ā  760W 41.1A ???kg
6S LiPo (11100 rpm) + 15x8 prop: Ā  1256W 56.6A ???kg
~~6S LiPo (11100 rpm) + 16x10 prop: Ā  669W 45.2A ???kg~~
4S LiPo (Ā  7400 rpm) + 16x10 prop: Ā  669W 45.2A ???kg
I used the wrong crossed out rating for the decisions below, so these are not entirely accurate. See iteration 4 for the right version.

Conclusion: OK

6. Turnigy Aerodrive SK3 - 5055-380KV Brushless Outrunner Motor#

https://hobbyking.com/en_us/outrunner-for-1450mm-spitfire-inc-prop-shaft-x-shared-part.html

Kv: 380
Max current: 65A
Price: ā‚¬42.73
Weight: 422g

Conclusion: maybe OK

Comparing all of the above seems a bit arbitrary, and I still have a lot to learn.

Regardless Iā€™ll be going with #5: the PROPDRIVE v2 4258 500KV Brushless Outrunner Motor (ā‚¬46.10) with 6S battery and 16x10 prop. It is the second cheapest shippable option, the lightest motor, and while using a larger prop and rpm, it achieves a lower power draw (669v869) than #1 (while likely providing more thrust).

Also, all reviews are positive and PROPDRIVEā€™s technical specifications seems more complete than Turnigyā€™s, which does inspire more confidence.

Stability and Control, Center of Mass, Aerodynamic Center and Static Margin#

I wonā€™t be calculating any of the stability paramters right now for two reasons:

  • I will be 3D printing the fuselage, which means I have a lot of freedom with regards to weight distribution and dihedral.

  • I donā€™t have any experience building wings, and to test out some of the weight distribution ideas that I have (like putting batteries in the front section of the wing), I feel like I have to build first.

Final parts selection#

Motor#

As outlined above, this will be the PROPDRIVE v2 4258 500KV Brushless Outrunner Motor (ā‚¬46.10).

ESC#

Assuming a 10% higher ESC power rating than the 60A max motor current (weā€™re only planning on 45.2A anyway), we need a 66A ESC.

I decided on the YEP 80A (2~6S) SBEC. Itā€™s well rated, can handle more than enough current, and has a nice 6A@5.5V BEC.

Battery#

Our max power draw is approximately 66A. This means weā€™re looking for a C rating of at least:
Or double that to be safe, as per https://www.rchelicopterfun.com/lipo-batteries.html#lipo3

  • 3000mAh: 22 (44)

  • 3300mAh: 20 (40)

  • 3700mAh: 18 (36)

  • 4000mAh: 17 (34)

Motocalc recommends a 2100 2P = 4200 pack system to get half an hour of flight time.

I decided to go with the Turnigy nano-tech 4000mAh 6S 35~70C. I was considering going with two lower capacity packs to integrate into the wing, however this would be difficult because the usual minimum thickness of a 6S pack is about 45mm. Also, this pack has a relatively high capacity-to-weight ratio of 6.61mAh/g, which is better than for example the Turnigy Heavy Duty 4000mAh 6S 60C at 5.87mAh/g. Iā€™m noticedI underestimated all power components quite a bit, so the relatively lighter weight will come in handy.

Prop#

The TGS Precision Sport Propeller 17x10 look ok. Iā€™m just now realizing how big 17 inches is. Since I need to do a new iteration with better weight estimates anyway I might also come back to this and try to pick a smaller prop diameter.