A i r c r a f t S
u p e r C a l c u l a t o r 7.0
calculation bug fixes with optimizations
for the Weedhopper ultralight ©2009, all rights reserved. |
| MAC And Neutral Point |
use the same units of measure for all entries!
|
Aerodynamic Center (AC)
is a fixed point on the wing located at 25% MAC and is basically
the PIVOT POINT of the wing. It is NOT the same as Center
of Lift/Pressure (COL/COP), which is a dynamic, moving point
based on the wing's Angle of Attack (AOA). COL is always
aft of AC and in a delta-shaped wing, can even be aft of
the TE during a stall.
Center of Gravity (CG)
is the point where the WEIGHT of the aircraft is balanced.
Neutral Point (NP) is the point where
the AERODYNAMIC FORCES generated by the wing and tail are
balanced.
25% - 35% MAC is generally
accepted as a good range for the CG of a conventional tailed
aircraft .
Placing CG 5% - 15% of
MAC in front of NP creates a longitudinal (pitch) stability
called Static Margin.
A lower margin (tail heavy) produces less stability and greater
elevator authority, while a higher margin (nose heavy)
creates more stability and less elevator authority. Too high
of a static margin results in elevator stall at take off and
landing.
|
The Equations
| Wing Sweep, C = |
|
(S * (A + 2B)) / (3 * (A + B)) |
| MAC (length) = |
|
A - (2 * (A - B) * (0.5 * A + B) / (3 * (A + B))) |
| MAC location, d = |
|
Y * ((A - MAC) / (A - B)) |
| wing area, WA = |
|
Y * (A + B) |
| tail area, TA = |
|
YY * (AA + BB) |
| wing aspect ratio, ARw = |
|
((Y * 2) ^ 2) / WA |
| tail aspect ratio, ARt = |
|
((YY * 2) ^ 2) / TA |
| Tail Arm = |
|
(D - wing AC) + tail AC |
| tail volume, Vbar = |
|
(TA / WA) * (Tail Arm / MAC) |
| NP (%MAC) = |
|
0.25 + (0.25 * sqr(sqr(ARw)) * Vbar |
| ideal CG (%MAC) = |
|
NP - Desired Static Margin |
| Moment (total) = |
|
(Lt wheel Wt * Lt Arm) + (Rt Wheel Wt * Rt Arm) + (Ctr Wheel Wt
* Ctr Arm) + (Pilot Wt * Pilot Arm) + ( Psngr Wt * Psngr Arm) + (Fuel
Wt * Fuel Arm) |
| actual CG (%MAC) = |
|
((Moment / Total Wt) - (Datum2LE + C)) / MAC |
| actual static margin % = |
|
(NP - actual CG) / MAC * 100 |
COPYRIGHT NOTICES:
- CG & MAC
equations adapted from the Public Domain.
- NP equations courtesy Alasdair Sutherland (see C.G.
Position article on Bloobird
Radio Flyers)
- Neutral Point and
Weight & Balance
Calculators developed by Dean A. Scott and are ©2005 -
2009, all rights reserved. Unauthorized use of the codebehind,
html, or content is strictly prohibitied.
Email the author at dascott / at /
chrusion / dot / com to obtain copyright clearances to redistribute,
repurpose, and/or reuse all or parts of the code and content
herein.
|
|
TESTIMONIALS:
I have been using your software/calculators to set up the
RC gliders that I build for myself. I had two planes go down
because of the lazy calculators that are out there. Since I
have found your calculator I have had nothing but success.
I just want to say, THANK YOU VERY MUCH!!!
David Field
|
|
| |
Wing |
Tail |
| Root Chord : |
(A)
|
(AA)
|
| Tip Chord : |
(B)
|
(BB)
|
| Sweep Distance : |
(S)
|
(SS)
|
| Half Span : |
(Y)
|
(YY)
|
| Distance
between wing & tail root LE's : |
(D)
|
| Aircraft
Type: (enter 1 for Weedhoppers, 0 for all others) : |
|
Desired Static Margin :
(5% = twitchy 15% = mushy 10% recommended) |
|
|
When making a change
in this section, be sure to also click the
Weight & Balance calculation button, too (but only if you've filled in that section).
|
| Weight And Balance |
| |
Weight |
Arm |
| Left Main Wheel : |
|
|
| Right Main Wheel : |
|
|
| Nose or Tail Wheel : |
|
|
| Pilot : |
|
|
| Passenger : |
|
|
| Fuel Tank (gallons of gas) : |
|
|
Datum
Point from Wing Root LE* (negative value is aft of the LE):
*LE bracket bolt hole on Weedhoppers |
|
|
|
| Calculated Results |
| Mean Aerodynamic Chord |
(MAC) = |
| MAC distance from root chord |
(d) = |
| Wing Aerodynamic Center aft of root LE |
(AC) = |
| Ideal Center of Gravity %MAC |
= |
| Ideal CG aft of root LE |
= |
| Actual Center of Gravity %MAC |
= |
| Actual CG aft of root LE |
= |
| Actual CG from main axle (neg. is aft) |
= |
| Neutral Point %MAC |
(NP) = |
| Neutral Point aft of Wing's root LE |
(NP) = |
| Distance between Ideal CG and NP |
(E) = |
| Distance between Actual CG and NP |
= |
| Desired Static Margin % |
= |
| Actual Static Margin % |
= |
| Gross Takeoff Weight of Aircraft |
= |
| Empty Weight of Aircraft |
= |
| Total Moment of Aircraft |
= |
| Other useful results |
| Wing Area = |
|
Tail Area = |
|
| Wing Apsect = |
|
Tail Aspect = |
|
| Wing Taper = |
|
Tail Taper = |
|
| Wing Sweep at MAC (C) = |
|
T sweep CC = |
|
| Tail MAC = |
|
T MAC dist = |
|
| Tail Arm = |
|
Vbar = |
|
| Lt wheel mnt = |
|
Rt wheel mnt = |
|
| Center wheel mnt = |
|
Pilot mnt = |
|
| Passngr mnt = |
|
Tank mnt = |
|
