Martin Pohl
CZAW CH601XLB Zodiac
Load Analysis
CZECH AIRCRAFT WORKS ZENAIR CH601XLB ZODIAC LOAD ANALYSIS
Issued by:
Martin Pohl eidg. dipl. (M.Sci.) Masch.Ing. ETH
Date:
Adress:
Blumenbergstrasse 7 CH8634 Hombrechtikon Switzerland
Version:
Contact:
Email:
[email protected] Web: www.pohltec.ch/ZodiacXL
Page 1
9. Februar 2014
1.3
Version 1.3 / 9.2.2014
Martin Pohl
CZAW CH601XLB Zodiac
Load Analysis
Table of Content
1 1.1 1.2 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8
OVERVIEW ................................................................................................................................................... 4 INTRODUCTION ............................................................................................................................................. 4 REGULATIONS............................................................................................................................................... 4 DEFINITIONS ............................................................................................................................................... 5 AIRCRAFT PARAMETER................................................................................................................................ 5 FORMULARY ................................................................................................................................................. 7 3VIEW DRAWING......................................................................................................................................... 8 WEIGHTS....................................................................................................................................................... 9 LIMIT LOAD FACTORS.................................................................................................................................. 9 CENTER OF GRAVITY ................................................................................................................................... 9 AIRSPEEDS .................................................................................................................................................. 10 VNDIAGRAM ............................................................................................................................................ 10 WING ............................................................................................................................................................ 11 WING GEOMETRY / WEIGHTS.................................................................................................................... 11 SPANWISE LIFT DISTRIBUTION .................................................................................................................. 12 SHEAR AND BENDING MOMENT ................................................................................................................. 14 SYMMETRICAL FLIGHT CONDITIONS ........................................................................................................ 15 LIFT + DRAG COMPONENTS ....................................................................................................................... 16 WING TORSION ........................................................................................................................................... 19 UNSYMMETRICAL FLIGHT CONDITIONS.................................................................................................... 20 GUST LOADING ........................................................................................................................................... 22
4
FUSELAGE .................................................................................................................................................. 23
5
HORIZONTAL TAIL .................................................................................................................................. 24
5.1 5.2 6 6.1 7 7.1 7.2 7.3 8
SURFACE LOADING CONDITION ................................................................................................................. 24 BALANCING LOAD ...................................................................................................................................... 24 VERTICAL TAIL ........................................................................................................................................ 26 SURFACE LOADING CONDITION ................................................................................................................. 26 CONTROL SURFACES .............................................................................................................................. 27 AILERON ..................................................................................................................................................... 27 WING FLAP ................................................................................................................................................. 27 AILERON + ELEVATOR TRIM TAB ............................................................................................................. 28 CONTROL SYSTEM .................................................................................................................................. 29
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Martin Pohl
9
CZAW CH601XLB Zodiac
Load Analysis
ENGINE MOUNT ........................................................................................................................................ 30
9.1
LOADS ON ENGINE MOUNT ......................................................................................................................... 30
10
GROUND LOADS ..................................................................................................................................... 31
10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8
STATIC GROUND LOAD CONDITIONS....................................................................................................... 31 LEVEL LANDING CONDITIONS TAILDOWN LANDING CONDITIONS ...................................................... 32 SIDE LOAD CONDITIONS........................................................................................................................... 33 BRAKED ROLL CONDITIONS .................................................................................................................... 33 SUPPLEMENTARY CONDITIONS FOR NOSE WHEEL ................................................................................. 33 LIMIT DROP TESTS ................................................................................................................................... 34 GROUND LOAD DYNAMIC TEST ............................................................................................................... 34 RESERVE ENERGY ABSORPTION .............................................................................................................. 34
11
REVISIONS ................................................................................................................................................ 35
12
REFERENCES ........................................................................................................................................... 35
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Martin Pohl
1
Overview
1.1
Introduction
CZAW CH601XLB Zodiac
Load Analysis
The CH601XLB is certified in many countries under different regulations: e.g. as an Ultralight Aircraft in Germany, as a Light Sport Aircraft in the USA or as an Experimental airplane in the UK. Therefore different load analysis’ for the Zenair/CZAW CH601XLB Zodiac were prepared by different aviation authorities. Chris Heintz, Zenair Aircraft and designer of the CH601XLB, prepared an extensive load and stress analysis for the CH601XL, which should be considered as the master analysis for the Zenair CH601XLB. The present load analysis was specifically prepared for certification of the CZAW CH601XLB in Switzerland, based on European regulations and on the layout of the CZAW CH601XLB. The CZAW CH601XLB was built by Czech Aircaft Works under licenseagreement with Zenair and has some minor changes compared to the original Zenair CH601XLB: • • •
1
Angle of incidence increased by 2° (better visibility during cruise flight) Rotax 912ULS engine (different weight than Continental O200 or Jabiru engine) Composite main gear legs (instead of aluminium gear legs)
This analysis was revised by two independent aviation engineers. Nevertheless it is of informal character only and the author doesn’t take any responsibility if parts of the analysis are incorrect.
1.2
Regulations
The following load analysis is based on the “Certification Specifications for Very Light Aircraft” issued by the European Aviation Safety Agency (EASA) [Ref]. References to CSVLA are given throughout this entire load analysis. CSVLA 1 CSVLA is valid for the following type of aircraft: •
Single engine (spark)
•
Max. 2 seats
•
MTOW not more than 750 kg
•
Stalling speed in landing configuration of not more than 45 kts
•
DayVFR only
CSVLA 301 (d) Simplified structural design criteria are defined in CSVLA, Appendix A, and are valid for aircraft with conventional configurations. AMC VLA 301 (d) In this context “aircraft with conventional configuration” means: •
Forward wing with an aft horizontal tail
•
Wing untapered or continuously tapered with no more than 30° fore or aft sweep
•
Trailing edge flaps may be fitted, but no winglets/tip devices, T/Vtail, slotted flap devices.
The CH601XLB Zodiac airplane satisfies all of these criteria. Therefore the “simplified design load criteria for conventional very light aircraft” CSVLA, Appendix A, can be applied and are used throughout this load analysis. 1
Today the newer Zenair CH601XLBs (and its successors CH650) provided by Zenair use the same increased angle of incidence and composite gear (Zenair Europe).
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CZAW CH601XLB Zodiac
2
Definitions
2.1
Aircraft Parameter
Load Analysis
Parameters in italic type are based on the original drawings of Zenith and CZAW and on aviation technology publications. Parameters in standard type are calculated values (formulary in a following subchapter). Fuselage (B) Fuselage Length: Fuselage Width (Cockpit):
LB = bB =
6,1 m 1,07 m
Wing (W) Overall Wing Span: Wing Span one Wing: Chord at Wingtip: Chord at Wing Root: Chord at Fuselage Center Line:
b= bW = c1 = cRoot = c0 =
8,23 m 3,58 m 1,42 m 1,60 m 1,626 m
Overall Wing Area: One Wing Area:
A= AW =
12,5 m² (incl. Fuselage Part and Flaps/Ailerons) 5,4 m² (incl. Flaps/Ailerons)
Mean Geometrical Chord: Mean Aerodynamical Chord: Wing Aspect Ratio: Sweep Angle at 25% Line: Taper ratio:
cmean = caero = ΛW = φ25° = λW =
1,523 m 1,525 m 5,40 0,72° 0,87
Anlge of incidence:
γW =
3°
Wing profile:
Riblet Wing GA 35A415 Thickness tmax = 15,0% at 35% (≈ 22,8 cm) Max. camber Y = 3,3% at 43% (≈ 5,0 cm)
Wing Profile Lift Curve Slope: Wing Lift Curve Slope: Maximum Lift Coefficient:
d(ca)/dα = d(cA)/dα = cLmax,Clean ≈ cLmax,FullFlaps ≈
6,3 rad 1 4,2 rad 1,82 2,3
[Ref. H. Riblett] [Ref. H. Riblett]
Wing Profile Zero Lift Angle:
αL=0 =
3,34°
[Ref. R. Hiscocks]
Wing Lift Aero Center: Wing Pitching Moment Coeff.:
at wing ¼ chord station (25%) cm(c/4) = 0,0587
[Ref. Zenithair]
Aircraft Aerodynamics Aircraft Drag Polar:
CD =
0,033 + 0,07·CL²
[Ref. R. Hiscocks]
Wing Flaps (F) 1 Flap Span: Flap Chord: 1 Flap Area:
bF = cF = AF =
2,03 m 0,335 m 0,68 m² (1 Flap only)
Flap Deflection:
δF =
0° / 30°
Wing Pitching Moment:
∆cm(C/4) =
0.18
1
Page 5
[Ref. R. Hiscocks]
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Martin Pohl
CZAW CH601XLB Zodiac
Ailerons (Ail) 1 Aileron Span: Aileron Chord: 1 Aileron Area:
bAil = cAil = AAil =
1,50 m 0,31 m 0,46 m² (1 Aileron only)
Aileron Deflection:
δAil =
±11,5°
Aileron Trim Tab Span: Aileron Trim Tab Chord: Aileron Trim Area:
bAilTrim = cAilTrim = AAilTrim =
0,538 m 0,072 m 0,039 m²
Horizontal Tail (HT) Elevator (Elev) HT Span: HT Chord: HT Area: HT Aspect Ratio: HT Arm (at 25% chord)
bHT = cHT = AHT = ΛHT = dHT =
2,3 m 0,8 m 1,84 m² (including Elevator) 2,96 3,25 m
HT Profile:
Load Analysis
HT Lift Curve Slope:
NACA 0012 Thickness tmax = 12% at 30% (= 100 mm) 1 d(ca)HT = 3,27 rad
Elevator Span: Elevator Chord: Elevator Area:
bElev = cElev = AElev =
2,2 m 0,35 m 0,77 m²
Elevator Deflection:
δElev =
+30° / 27°
Elevator Trim Span: Elevator Trim Chord: Elevator Trim Area:
bElevTrim = cElevTrim = AElevTrim =
0,897 m 0,062 m 0,056 m²
Rudder (R) Rudder Span: Rudder Chord Tip: Rudder Chord Bottom: Rudder Aspect Ratio: Rudder Arm (Wing > R) Rudder Area Surface:
bR = cR1 = cR0 = ΛR = dR = AR,Surface =
1,42 m 0,37 m 0,98 m 2,25 3,90 m 0,52 m² (moving rudder surface only)
Rudder Profile:
NACA 0012 Thickness tmax = 45 (tip)  105 mm (root)
Rudder Deflection:
δR =
±20°
Flight Control System Aileron – Control Stick: Aileron – Wing Bell Crank: Aileron – Rudder Horn:
Pilot: 330 mm / Control: 80 or 100 mm To Stick: 80 mm / To Aileron: 85 mm 100 mm
Elevator – Control Stick: Elevator – Rudder Horn:
Pilot: 330 mm / Control: 120 mm 100 mm
Rudder – Pedals: Rudder – Rudder Horn:
Pilot: 190 mm / Control: 65 mm 125 mm
Control Cables Tension:
110 N
Engine Mount Attachment Bolt:
AN6
Seat Belts Attachment Bolt: Thickness Attachment Plate:
AN55A 0,040” = 1 mm Page 6
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Martin Pohl
2.2
CZAW CH601XLB Zodiac
Load Analysis
Formulary
Most of the following formulas are selfexplanatory and are all based on the geometry of the Zodiac CH601XLB.
b − bB 2
Wing Span one Wing:
bW =
Chord at Fuselage Center:
c0 = c Root +
Wing Area:
AW =
Mean Geometrical Chord:
cmean =
c0 + c1 2
Mean Aerodynamical Chord:
c aero =
2 c0 + c0 c1 + c1 3 c 0 + c1
Wing Aspect Ratio:
ΛW =
2b c0 + c1
Sweep Angle at 25% Line:
ϕ 25° =
c −c 1 ⋅ arctan 0 1 4 b 2
Wing Taper Ratio:
λW =
Wing Profile Lift Curve Slope:
d (c a ) = 2π dα
Wing Lift Curve Slope:
ΛW d (c A ) = 0.1 ⋅ dα ΛW + 2
Wing Profile Zero Lift Angle:
α L =0 = −100 ⋅
c Root − c1 b ⋅ 2 bW
c0 + c1 ⋅b 2
2
2
Straight wing leading edge
c1 c0
Y X − 3 .2 ⋅ + 1 .4 c c
Page 7
max. chamber Y at pos. X
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Martin Pohl
2.3
CZAW CH601XLB Zodiac
Load Analysis
3View Drawing
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Martin Pohl
2.4
CZAW CH601XLB Zodiac
Load Analysis
Weights
CSVLA 25 (a) (b) Compliance with each applicable requirement (structural loading and flight requirements) of CSVLA at both maximum and minimum weight has to be shown. (a) Maximum weight has to be highest of: •
Each seat occupied (2 x 86kg), at least enough fuel for 1 h of flight with max. continuous power (25 L ~ 20 kg), whereas empty weight is W ZFW = 340 kg (approx.): W max,1 = 340 + 2 x 86 + 20 = 532 kg
•
One pilot (86 kg), full fuel (180 L = 135 kg): . W max,2 = 340 + 86 + 135 = 561 kg
•
Design weight:
Wmax =
600 kg
(b) Minimum weight is ZFW + one light pilot (55 kg) + ½ h of flight with max. continuous power: Wmin = 340 + 55 + 10 = 405 kg 2
CSVLA 321 (b)(2) “Compliance with the flight load requirements must be shown […] at each practicable combination of weight and disposable load within the operating limitations specified in the Flight Manual”. Although not part of Appendix A, this requirement can be taken as a guideline for how the fuel distribution in the wing has to be taken into account for the load calculations. Most critical case is at maximum weight and minimum fuel. CSVLA A7 (a) Based on the simplified criteria (Appendix A) only the maximum design weight condition must be investigated.
2.5
Limit Load Factors
CSVLA A3 / A7 (b)(c) The limit flight load factors (normal catergory) are: Positive manoeuvering limit load factor: Negative manoeuvering limit load factor: Positive gust limit load factor at vC: Negative gust limit load factor at vC:
n1 = 3,8 n2 = 1,9 n3 = 3,8 n4 = 1,9
Positive limit load factor with flaps fully extended at vF: nflap = 1,9
2.6
Center of Gravity
CSVLA A7 (d) Mean C.G.: Forward C.G.: Rearward C.G.:
2
xCG = eFwd = eAft =
25% = 380 mm (based on MAC = 1,52 m) 5% = 76 mm / 304 mm +5% = 76 mm / 456 mm
CSVLA 321 is not part of and not required under CSVLA Appendix A. Page 9
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Martin Pohl
2.7
CZAW CH601XLB Zodiac
Load Analysis
Airspeeds
CSVLA A3 / A7 (e)(2)
2.8
Design speed
CSVLA (min)
CH601XLB
Minimum design flap speed: Minimum design maneuvering speed: Minimum design cruising speed: Minimum design dive speed:
VF,min = 70 kts VA,min = 95 kts VC,min = 107 kts VD,min = 151 kts
vF = 70 kts vA = 95 kts vC = 107 kts vD = 156 kts
Stall speed clean: Stall speed full flaps:
vS = 40 kts vS0 = 35 kts
Never exceed speed:
vNE = 140 kts
VnDiagram
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Martin Pohl
CZAW CH601XLB Zodiac
3
Wing
3.1
Wing Geometry / Weights
Load Analysis
The wing of the CH601XLB is made up of a main spar, a rear spar and 10 wing ribs. Two 45 L (12 USG) fuel tanks are placed in front of the main spar, between nose ribs NR4/NR5 and NR5/NR7 (extended range version, the standard version has 1x 12 USG tank per wing).
Position of Wing Ribs Y is the distance between the rib and the aeroplane center line [in mm]. Rib #
#0
#f
#4
#5
#6
#7
#8
#9
#10
Position Y [mm]
0
507
862
1382
1902
2422
2982
3732
4122
Wing Dry Weight Distribution The dry weight of the wing is split up in several sections (e.g. section 8 = between ribs #8 and #9). Each section weight includes the corresponding wing structure, primer, paint and all systems installed (e.g. strobe light transformer). Section
0
f
4
5
6
7
8
9
Wing
(7 kg)
4 kg
6 kg
6 kg
6 kg
6 kg
5 kg
6 kg *)
+ Fuel Tanks


1,5 kg
1,5 kg
1,5 kg
1,5 kg


45 kg
Fuel Min Fuel


5 kg
0 kg
0 kg
0 kg


50 kg
Fuel Max Fuel


17 kg
17 kg
17 kg
17 kg


113 kg
Page 11
Total
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Martin Pohl
3.2
CZAW CH601XLB Zodiac
Load Analysis
Spanwise Lift Distribution
In general the spanwise lift distribution can be divided into: • • •
Base lift distribution Lift distribution due to wing twist Additional lift distribution due to flaps and/or ailerons
Base Lift Distribution According to Schrenk [Ref] the base lift load at any selected spanwise station is the arithmetical mean between the load which is proportional to the chord of the real wing and the load which is proportional to the chord of an elliptical wing with equal wing area. It can be assumed that the lift distribution is continuative over the entire wingspan, including the fuselage [Schlichting/Truckenbrodt, Ref]. The lift of the fuselage is substituted by the lift of the (fictive) wing centerpiece. The formula’s numbering [in brackets] corresponds to the numbers of the resultstable on a next page.
y b 2
Relative spanwise position:
y=
Chord tapered wing:
c wing ( y ) = c0 −
[1]
c0 − c1 ⋅y b 2
c wing ( y ) = 1,627 −
Chord elliptical wing:
cell ( y ) = c0,ell
with
1,627 − 1,42 ⋅ y = 1,627 − 0,0503 ⋅ y 8,23 2
y ⋅ 1 − b 2
c0,ell = c0,ell =
[2]
2
[3]
c0 + c1
π 1,627 + 1,42
π
= 0,970
y cell ( y ) = 0,970 ⋅ 1 − 4,115 Mean chord:
c mean ( y ) =
c wing ( y ) + cell ( y ) 2
2
[4]
The drawing on the following page shows the chord of the original CH601XLBwing c(wing), the chord of the surrogate elliptical wing with identical wing area c(0,ell) and the mean value of the two chord lines c(mean). According to Schrenk [Ref], c(mean) is proportional to the spanwise lift distribution.
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CZAW CH601XLB Zodiac
Load Analysis
Original Chord and Chord of Surrogate Elliptical Wing 2000 1800 1600
Chord [mm]
1400 1200
c(wing)
1000
c(0,ell) c(mean)
800 600 400 200 0 0
1000
2000
3000
4000
Spanwise Position [mm]
For the sake of convenience, the wing is split up in several sections to calculate the spanwise lift distribution (similar to the wing dry weight distribution).
c mean ( y i ) + c mean ( y i +1 ) 2
Mean chord of one section:
ci =
Width of one section:
∆y i = y i +1 − yi
[6] [7]
The wing lift for one specific section can be calculated by multiplying the total lift required with the ratio between the section area and the total wing area: Wing lift of one section:
∆Li =
ci ⋅ ∆y i ⋅ Ltotal ,required AW
[8]
Lift due to Wing Twist The ailerons are twisted 2,5° up along the trailing end, which corresponds to a wing twist of closely 1,25° over the aileron span. It is therefore conservative to consider a wing without twist for calculation of the maximum wing bending moment. Additional Lift with Flaps Extended CSVLA A9 (b)(2) With flaps extended the lift coefficient at the corresponding wing section is increased by approx. 1,0. However it is obvious that the shear and bending moment on each wing is considerably lower because of the reduced load factor of n = +1,9 / 0,0 with flaps extended. Therefore the case with flaps extended will not be further investigated regarding shear and bending moment.
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Martin Pohl
3.3
CZAW CH601XLB Zodiac
Load Analysis
Shear and Bending Moment
Shear and bending moment of the wing are again calculated for the same discrete sections of the wing, starting from wing tip to wing root. It is obvious that the higher the lift forces the higher the stress on the wing. On the contrary the inertia force of the wing (masses) act as a relieving factor and unload the stress on the wing.
Wing Lift Shear due to lift at rib:
Ti = Ti +1 + ∆Li
Bending moment due to lift at rib:
M i = M i +1 + ∆y i ⋅ Ti +1 +
[9]
∆yi ⋅ ∆Li 2
[10]
Wing Inertia Relief Wing inertial relief force of one section: ∆Wi
= ∆Wi ,Wing + ∆Wi , Fuel
Inertia relief at rib:
T − i = T − i +1 + ∆Wi
Inertia relief bending moment at rib:
M − i = M − i +1 + ∆y i ⋅ T − i +1 +
[13] [14]
∆y i ⋅ ∆Wi 2
[15]
Total Shear and Bending Moment Shear at rib:
Ti ,lim it = Ti + T − i
[16]
Bending moment at rib:
M i ,total = M i + M − i
[17]
Ultimate shear:
Ti ,ult = 1,5 ⋅ Ti ,lim it
[18]
Ultimate bending moment:
M i ,ult = 1,5 ⋅ M i ,lim it
[18]
Ultimate Loads
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Martin Pohl
3.4
CZAW CH601XLB Zodiac
Load Analysis
Symmetrical Flight Conditions
CSVLA A9 (b)(1)(i) (ii) The calculation of wing lift, wing inertia relief, shear and bending moment for the symmetrical flight condition is performed by using an excel calculation sheet. The results for MTOW = 600 kg and 20 L of fuel (most critical/conservative loading with ½ hour of fuel and 5 L unusable fuel) are shown below. The down force of the horizontal tail is assumed to be 5% of the total wing lift.
Input Parameters Zodiac CH601XLB c0 Yellow fields are input parameters! 1626 [mm] c1 [mm] 1420 c(0,ell) 1939 [mm] b/2 [mm] 4122 A(w,total) 12,6 [m²] Load Factor 5% of wing lift [] 3,8 L(req,total) TOW 600 kg 22358 HT 1118 [N] 23476 f(corr.) [] 1,00715 Rib/Section Wing Geometry 1Y/(b/2) 2Y 3c(wing) 4c(ell) 5c(mean)
#
0
f
4
5
6
7
8
TOTAL
9
10
[] [mm] [mm] [mm] [mm]
0,00 0,12 0 507 1626 1601 1939 1924 1783 1763
0,21 862 1583 1896 1740
0,34 1382 1557 1827 1692
0,46 1902 1531 1720 1626
0,59 2422 1505 1569 1537
0,72 2982 1477 1339 1408
0,91 3732 1439 823 1131
Wing Lift (Flaps up) 6c(i) [mm] [mm] 7dy(i) 8dL(i) [N] 9T(i) [N] 10M(i) [Nm]
1773 1751 507 355 1692 1171 11738 10046 22001 16479
1716 520 1680 8875 13120
1659 520 1624 7195 8942
1581 520 1548 5571 5623
1472 560 1553 4022 3129
1270 750 1793 2469 1311
921 390 676 676 132
7,5 0 279 1248 1597
7,5 0 279 969 1020
7,5 0 279 689 589
5
6
261 149 2217 1956 4117 3059
7,5 10 559 1807 2391
186 410 281
224 224 44
Total Shear / Bending Moment 16T(limit) [N] 9521 8089 17M(limit) [Nm] 17884 13420
7068 10729
5947 7346
4602 4603
3333 2540
2059 1030
453 88
18T(ultimate) 19M(ultimate)
10602 16094
8920 11018
6903 6905
4999 3810
3089 1545
679 132
Wing Weight 11Wing 12Fuel 13dW(i) 14T(i) 15M(i)
[kg] [L] [N] [N] [Nm]
[N] [Nm]
7
4
14281 12134 26826 20129
23476
1,00 4122 1420 0 710
The resulting maximum shear and bending moment at the wing root are highlighted in amber (limit) and red (ultimate) color.
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CZAW CH601XLB Zodiac
Load Analysis
For comparison the results for different MTOW and fuel quantities are summarized in the following table. The considered cases are: 1. MTOW = 600 kg, minimum fuel (1/2 h + unusable fuel): therefore the load inside the fuselage is 260 kg (useful load) – 15 kg (fuel) = 245 kg. 2. MTOW = 600 kg, full tanks (180 L): the remaining dry load is 260 kg (useful load) – 135 kg (full fuel) = 125 kg. 3. Two standard persons aboard (2 x 86 kg) + full inner tanks (90 L) TOW = 580 kg. 4. One person aboard (86 kg) + minimum fuel (20 L) TOW = 440 kg.
1
2
3
4
TOW Fuel Quantity
[kg] [L]
600 20
600 180
580 90
440 20
T(limit)
[N]
8089
5853
6776
5410
[Nm] [N] [Nm]
13420 12134 20129
10070 8780 15105
11942 10164 17913
9025 8116 13538
M(limit) T(ultimate) M(ultimate)
Case 1 is critical (MTOW = 600 kg, minimum fuel = 20 L).
3.5
Lift + Drag Components
For a structural analysis of the airplane, it is important to determine the forces acting on the wing. The wing lift is balancing the weight/inertia forces of the airplane, whereas (in horizontal, steady flight) the drag is overcome by the thrust of the engine. In order to be able to properly analyze the structure of the wing, the lift L and drag D are normally converted into their resulting force R. In addition the tangential force acting on the wing T is calculated, which is the component of R along the wing axis. It is not obvious from the very first in which direction the tangential force T is pointing to. A discussion of results at different airspeeds and load factors is therefore of high importance.
Lift, drag and the corresponding resulting force as well as the tangential force acting on the wing are calculated by using the formulas below. The wing forces are all a function of airspeed and load factor. Therefore different cases from the vndiagram are considered, i.e. at the points A, D, G and E. The formula’s numbering [in brackets] corresponds to the numbers of the resultstable on a next page.
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CZAW CH601XLB Zodiac
Load Analysis
Wing Lift Wing lift curve slope:
d (c L ) Λ = 0,1 ⋅ dα Λ+2
[1]
Total lift
Ltotal = n ⋅ W ⋅ 105%
[2]
The total lift includes an assumed 5% additional lift for counteracting the horizontal tail down force. Lift 1 wing:
L1Wing = Ltotal ⋅
Lift coefficient:
cL =
α=
A
L1Wing
ρ 2
Angle of attack:
A1Wing
[3]
[4]
2
v ⋅ A1wing
cL d (c L ) dα
[5]
The wing weight (i.e. the inertia forces of the wing) can be subtracted from the wing lift: Inertia relief 1 wing:
I 1wing = − n ⋅ W1Wing
[6]
Net shear load 1 wing:
T1wing = L1Wing + I 1Wing
[7]
Wing Drag The inertia forces in the direction of the wing axis are small compared to the wing drag. Therefore they are neglected in this calculation. 2
Drag coefficient:
c c D = 0,01 + L π ⋅Λ
Drag 1 wing:
D = cD ⋅
ρ 2
v 2 ⋅ A1Wing
[8]
[9]
Resulting Force Resulting total force:
R = L2 + D 2
[10]
Tangential Force
D L
Angle between L and R:
β = arctan
[12]
Angle between R and perpendicular of wing:
ϕ =α −β
[13]
Forward tangential force on 1 wing:
T1Wing = R ⋅ sin (ϕ )
[14]
Ultimate tangential force on 1 wing:
T1Wing ,ult = 1,5 ⋅ T1Wing
[15]
The results for different airspeeds and load factors according to the vndiagram are summarized in an exceltable on the next page.
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Load Analysis
LIFT + DRAG FORCES Aspect Ratio Total Wing Area Wing Area 1 Wing MTOW Weight 1 Wing
Λ A Aw W Ww
[m²] [m²] [kg] [kg]
5,4 12,5 5,4 600 44
[kts] [m/s] []
95 48,9 1,0
95 48,9 3,8
95 48,9 1,9
156 80,3 1,0
VD 156 80,3 3,8
156 80,3 1,9
0,073 6178 2669 0,338 4,6 431 2237
0,073 23476 10141 1,284 17,6 1640 8502
0,073 11738 5071 0,642 8,8 820 4251
0,073 6178 2669 0,125 1,7 431 2237
0,073 23476 10141 0,476 6,5 1640 8502
0,073 11738 5071 0,238 3,3 820 4251
0,017 132
0,107 846
0,034 271
0,011 233
0,023 498
0,013 284
Airspeeds / Load Factors Speed
vA v
Load Factor Wing Lift 1 Lift curve slope 2 Total Lift (incl. 5% HTLoad) 3 Lift 1 Wing 4 Lift coefficient 5 Angle of attack 6 Inertia Relief 1 Wing 7 Net Shear Load 1 Wing Wing Drag 8 Drag coefficient 9 Drag 1 Wing Resulting Force 10 Resulting Force 11 % of L Tangential Force 12 Angle between L and R 13 Angle between R and n_Wing 14 Fwd Tangential Force on 1 Wing 15 Ultimate Tangential Force 1 Wing
n
d(cL)/dα L [N] Lw [N] cL α [°] Iw [N] Tw [N]
cD Dw
[N]
R
[N]
β φ T
[°] [°] [N]
3,4 1,2 49
5,7 11,9 1763
3,6 5,2 382
5,9 4,2 166
3,3 3,2 472
3,8 0,6 42
T,ult [N]
73
2644
574
248
707
63
2241 8544 4260 2249 8516 4260 100,2% 100,5% 100,2% 100,5% 100,2% 100,2%
The maximum ultimate forward tangential force F = 2’644 N occurs at vA and n = 3.8. The maximum ultimate rearward tangential force F = 574 N occurs at vA and n = 1.9.
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3.6
CZAW CH601XLB Zodiac
Load Analysis
Wing Torsion
The wing torsion, which acts at each wing section and which is computed relative to the wing shear center (defined at 23% chord), consists of the following components: • • • •
Aerodynamic wing moment Moment due to wing lift force Moment due to wing structure weight Moment due to fuel weight.
Aerodynamic wing moment:
M c / 4 = c m ,c / 4 ⋅ with
Wing torsion moment:
ρ 2
v 2 ⋅ A1Wing ⋅ c mean
cm,c/4 = 0,0587 and cm,c/4,flaps = 0,25 A1Wing = 5,4 m², cmean = 1,52 m
M Torsion = M c / 4 − ∆ Lift ⋅ LWing + ∆ Wing ⋅ WWing − ∆ Fuel ⋅ WFuel with
∆Lift = 0,4 – 0,375 = 0,025 m ∆Wing = 0,7 – 0,375 = 0,325 m ∆Fuel = 0,375 – 0,3 = 0,075 m
It is obvious that the wing torsion depends on airspeed and load factor. Therefore calculations for different points of the flight envelope (A, D, E and G) have to be performed.
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Load Analysis
The results are summarized in the following table: Wing Torsion Lift(1 wing) W(1 wing) Fuel(1 wing) c(M,c/4) c(M,c/4,flaps)
Speed 259,2kg 44kg 90Liter 0,0587 0,25
vF vA vD
[m/s] 36,0 36,0 48,9 48,9 80,3 80,3
n [] 1,0 1,9 1,0 3,8 1,0 3,8
M(T,wing) M(T,total) [Nm] [Nm] 1630 1603 1630 1579 705 678 705 602 1901 1874 1901 1798
The critical case is at vD and n = 1,0 (highlighted in red). The ultimate torsion moment is: Ultimate torsion moment:
3.7
M Torsion ,ult = 1,5 ⋅ M Torsion ,lim = 1,5 ⋅ −1'874 Nm = −2'811Nm
Unsymmetrical Flight Conditions
CSVLA A9 (c)(3) According to regulations (CSVLA Appendix A) the wing has to withstand a combination of 75% of the positive maneuvering wing loading on both sides and the maximum wing torsion resulting from aileron input. Portion of wing with aileron: Aw,ail = 2,3 m² bail = 1,47 m Portion of wing without aileron: Aw.clear = 3,1 m² bclear = 1,57 m Aileron deflections: δup = + 11,5° δdown =  11,5°
The method of calculation for the effect of aileron displacement on wing torsion is described in CSVLA Appendix A. Step 1: Determination of critical airspeed / aileron deflection Total aileron deflection at vA:
∆ A = δ up + δ down = 11,5° + 11,5° = 23°
Total aileron deflection at vC:
∆C =
Total aileron deflection at vD:
∆ D = 0,5 ⋅
vA 48,9 ⋅∆A = ⋅ 23° = 20,0° vC 55,0 vA 48,9 ⋅ ∆ A = 0,5 ⋅ ⋅ 23° = 7,0° vD 80,3
Kfactor:
∆ c m 0 − 0,01 ⋅ D 2 K= ∆ c m 0 − 0,01 ⋅ C 2
7 ,0 2 ⋅ vD − 0,0587 − 0,01 ⋅ 2 80,3 2 − 0,0973 80,3 2 = ⋅ = ⋅ = 1,30 20,0 55,0 2 − 0,1587 55,0 2 2 ⋅ vC − 0,0587 − 0,01 ⋅ 2
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Load Analysis
Step 2: Calculation of aerodynamic torsion moment at vD: K > 1, therefore aileron deflection ∆D at vD is critical and must be used in computing wing torsion loads over the aileron span. Modified cm, aileron up:
c m,up = c m 0 + 0,01 ⋅ δ up = −0,0587 + 0,01 ⋅ 3,5 = −0,0237
Modified cm, aileron down:
c m,down = c m 0 − 0,01 ⋅δ down= −0,0587 − 0,01 ⋅ 3,5 = −0,0937
The torsion moment of the wing is calculated for the inner section of the wing without aileron (Mclear) and the outer section of the wing with deflected aileron (Mail). Torsion moment clear:
M clear = c m 0 ⋅
ρ 2
2
v D ⋅ Aw,clear ⋅ bclear
M clear = −0,0587 ⋅ Torsion moment aileron:
M ail = c m,up / down ⋅
1,225 80,3 2 ⋅ 3,1 ⋅ 1,57 = −1'128 Nm 2
ρ 2
M ail ,up = −0,0237 ⋅
1,225 80,3 2 ⋅ 2,3 ⋅1,47 = −316 Nm 2
M ail ,down = −0,0937 ⋅ Total aerodynamic moment:
2
v D ⋅ Aw,ail ⋅ bail
1,225 80,3 2 ⋅ 2,3 ⋅ 1,47 = −1'251Nm 2
M = M clear + M ail M up = −1'128 − 316 = −1'444 Nm M down = −1'128 − 1'251 = −2'379 Nm
Step 3: Calculation of total torsion moment at vD and 75% positive normal load (n=3,8): Wing lift at 75% normal load (1 wing):
L75% = 75% ⋅ L1wing = 0,75 ⋅ 10'046 N = 7'535 N
Wing inertia relief at 75% normal load: W75%
= 75% ⋅ WWing = 0,75 ⋅ (−1'640 N ) = −1'230 N
Fuel inertia relief at 75% normal load:
F75% = 75% ⋅ WFuel = 0,75 ⋅ (−2'513 N ) = −1'885 N
Total torsion moment:
M T = M − ∆ Lift ⋅ L75% + ∆ Wing ⋅ W75% − ∆ Fuel ⋅ F75%
M T ,down = −2'379 N − 0,025m ⋅ 7'535 N + 0,325m ⋅ 1'230 N − 0,075m ⋅ 1'885 N = −2'309 Nm M T ,up = −1'444 N − 0,025m ⋅ 7'535 N + 0,325m ⋅ 1'230 N − 0,075m ⋅ 1'885 N = −1'374 Nm Step 4: Ultimate loads: Ultimate asymmetric torsion moment:
M T ,up ,ult = 1,5 ⋅ M T ,up = −3'463 Nm M T ,down ,ult = 1,5 ⋅ M T ,down = −2'061Nm
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3.8
CZAW CH601XLB Zodiac
Load Analysis
Gust Loading
CSVLA 333 (not required for Appendix A) The gust loading of the wing can be calculated according to CSVLA 333 (however, not required for CSVLA Appendix A). Gust loads are considered as follows: •
at VC: gusts of Ude = 15.24 m/s
•
at VD: gusts of Ude = 7.62 m/s.
Critical aircraft weights are MTOW (W max = 600 kg) and minimum weight (W min = 405 kg).
ρ0 Gust load calculation (CSVLA 333):
n = 1+ 2
Kg =
µg =
⋅ v ⋅ a ⋅ K g ⋅ U de W ⋅g
S
0.88 ⋅ µ g 5 .3 + µ g 2 ⋅W
S d (c L ) ρ ⋅ c mean ⋅ dα
The results are summarized in the following table: Acft Weight [kg] MTOW 600 Wmin 405 MTOW 600 Wmin 405
Airspeed [m/s] vC 55 vC 55 vD 55 vD 55
Gust Ude Ude Ude Ude
[m/s] 15,24 15,24 7,62 7,62
ug 12,48 8,42 12,48 8,42
Kg 0,6176 0,5401 0,6176 0,5401
ng(pos)
ng(neg)
3,78 4,61 2,39 2,80
1,78 2,61 0,39 0,80
Remarks for case 2 (Wmin = 405 kg, vC = 55 m/s) In case 2 the load limit of the flight envelope is exceeded. The calculation of the wing shear and bending moment at W min = 405 kg and n = +4,61 gives the following result: Limit shear load: Ultimate shear load:
5’853 N 8’779 N
Limit bending moment: Ultimate bending moment:
9’783 Nm 14’674 Nm
The loads at W min = 405 kg and n = +4,61 are much lower than at MTOW = 600 kg and n = +3,8. However the local supporting structure for dead weight items needs to withstand the limit load of n = +4,61.
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4
CZAW CH601XLB Zodiac
Load Analysis
Fuselage
CSVLA A9 The fuselage has to be load tested according to CSVLA, similar to the wing load tests. The required loads on the fuselage are equal to the loads calculated for the engine mount, wing, horizontal tail and vertical tail. An example of fuselage loading is shown on the following drawing:
The required ultimate loads are: Engine: Cabin floor: Fuselage tail:
F1'687 = 1.5 ⋅ 2'870 N = 4'305 N (see chapter 9 Engine Mount) m FKAB = 1.5 ⋅ 3.8 ⋅ (2 ⋅ 86kg ) ⋅ 9,806 2 = 9'607 N s FVOP = 3'270 N (see chapter 5 Horizontal Tail)
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CZAW CH601XLB Zodiac
5
Horizontal Tail
5.1
Surface Loading Condition
Load Analysis
CSVLA A11 (c)(1) The average limit loading of the horizontal tail can be calculated according to CSVLA Appendix A, Table 2 and Figure A4:
W lb kg = 24,68 2 = 120,8 2 S ft m
Simplified limit surface distributions:
wHT = 4,8 + 0,109 ⋅ n1 ⋅
Simplified limit surface loading:
LHT ,lim = AHT ⋅ wHT ⋅ g = 1,84 ⋅ 120,8 ⋅ 9,806 = 2'180 N
Ultimate surface loading:
LHT ,ult = 1,5 ⋅ LHT ,lim = 3'270 N
The load must be distributed on the horizontal tail as follows: 3'270 N
2’126 N
5.2
Balancing Load
For comparison/confirmation of the simplified criteria, a detailed calculation for the balancing load is performed. The horizontal tail acts with a downward force against the forward nick moment and keeps the airplane in balance. Instead of using the simplified criteria of CSVLA Appendix A (Chapter 3) the following, more detailed analysis may be used: L .............. Wing Lift MW ........... Wing Nick Moment P .............. Horizontal Tail Lift W⋅n .......... Inertial Weight Force xCG ........... Center of Gravity (behind wing L.E.) xA ............ Center of Lift (behind wing L.E.) xHT.......... Arm to H.T. Center of Lift
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CZAW CH601XLB Zodiac
Equilibrium of moment at wing L.E.:
0 = M W + x A ⋅ L − xCG ⋅ n ⋅ W + x HT ⋅ P
Equilibrium of forces:
0 = −n ⋅ W + L + P
Zero Lift Moment:
M W = c m ,c / 4 ⋅ c mean ⋅
ρ 2
Load Analysis
v 2 ⋅ A2Wing
cm,c/4 = 0,0587, cmean = 1,523 m, ρ = 1,225 kg/m³, A2 = 12,5 m²
P=
Force on horizontal tail:
M W + ( xCG − x A ) ⋅ n ⋅ G x HT
The results for the balancing loads on the HT are summarized in the following table: v
CG
n
Pb [N] 1,0 3,8 1,9 1,0 3,8 1,9
v vD vD vD vD vD vD vD
fwd fwd fwd aft aft aft
v
CG
n 0,0 1,0 3,8 1,9 1,0 3,8 1,9
Pb [N] 1190 1336 1746 912 1065 714 1428
vA vA vA vA vA vA
fwd fwd fwd aft aft aft
v
CG
vC vC vC vC vC
fwd fwd fwd aft aft
1,0 3,8 1,9 1,0 3,8
706 1115 282 435 84
vF vF vF vF vF
fwd fwd fwd aft aft
1,0 1,9 0 1,0 1,9
1167 1298 1021 895 782
vC
aft
1,9
798
vF
aft
0,0
1021
n
588 997 164 316 35 680
CG
Pb [N]
n
Pb [N]
The maximum balancing load on the horizontal tail appears to be at vD, forward C.G. and n = 3,8. Ultimate HT balancing load:
Pb ,ult = 1,5 ⋅ Pb = 1,5 ⋅ −1'746 N = −2'619 N
The resulting ultimate load is lower than the result from the simplified calculation according to CSVLA.
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CZAW CH601XLB Zodiac
6
Vertical Tail
6.1
Surface Loading Condition
Load Analysis
CSVLA A11 (c)(1) The average limit loading of the vertical tail can be calculated according to CSVLA Appendix A, Table 2 and Figure A4:
W lb kg = 22,37 2 = 109,4 2 S ft m
Simplified limit surface distributions:
wVT = 1,656 ⋅ n1 ⋅
Simplified limit surface loading:
LVT ,lim = AVT ⋅ wVT ⋅ g = 0,52 ⋅ 109,4 ⋅ 9,806 = 558 N
Ultimate surface loading:
LVT ,ult = 1,5 ⋅ LVT ,lim = 837 N
The load must be distributed on the horizontal tail as follows:
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Martin Pohl
7
CZAW CH601XLB Zodiac
Load Analysis
Control Surfaces
CSVLA A11 (c)(1) The average limit loading of the control surfaces can be calculated according to CSVLA Appendix A, Table 2 and Figure A5.
7.1
Aileron W lb kg = 17,33 2 = 84,8 2 S ft m
Simplified limit surface distributions:
w Ail = 0,095 ⋅ n1 ⋅
Simplified limit surface loading:
L Ail ,lim = AAil ⋅ w Ail ⋅ g = 0,46 ⋅ 84,8 ⋅ 9,806 = 383 N
Ultimate surface loading:
L Ail ,ult = 1,5 ⋅ L Ail ,lim = 575 N
The load must be distributed on the aileron as follows:
7.2
Wing Flap
Simplified limit surface distributions:
wFlap = 0,131 ⋅ n1 ⋅
W c n , flap lb kg ⋅ = 17,92 2 = 87,7 2 S 1,6 ft m
with cn,flap = 1,2 Simplified limit surface loading:
LFlap ,lim = AFlap ⋅ wFlap ⋅ g = 0,68 ⋅ 87,7 ⋅ 9,806 = 585 N
Ultimate surface loading:
LFlap ,ult = 1,5 ⋅ LFlap ,lim = 878 N
The load must be distributed on the wing flap as follows:
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Martin Pohl
7.3
CZAW CH601XLB Zodiac
Load Analysis
Aileron + Elevator Trim Tab
Simplified limit surface distributions:
wTab = 0,16 ⋅ n1 ⋅
W c n ,tab lb kg ⋅ = 29,18 2 = 142,8 2 S 0,8 ft m
with cn,tab = 0,8 Simplified limit surface loading:
L AilTab ,lim = AAilTab ⋅ wTab ⋅ g = 0,039 ⋅ 142,8 ⋅ 9,806 = 49,6 N LElevTab ,lim = AElevTab ⋅ wTab ⋅ g = 0,056 ⋅ 142,8 ⋅ 9,806 = 78,4 N
Ultimate surface loading:
L AilTab ,ult = 1,5 ⋅ LTailTab ,lim = 74 N LElevTab ,ult = 1,5 ⋅ LElevTab ,lim = 118 N
The load must be distributed on the trim tabs as follows:
See „wing flap loading“
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8
CZAW CH601XLB Zodiac
Load Analysis
Control System
CSVLA A13 (a)(2) The acceptable limit pilot forces can be used as requirement for the control system strength. CSVLA 397 (b) The minimum and maximum limit pilot forces are as follows: Aileron limit force (control stick):
178 .. 300 N
Elevator limit force (control stick):
445 .. 740 N
Rudder limit force (pedals):
580 .. 890 N
In addition the rudder control system must withstand a simultaneous forward force of 1’000 N on both pedals.
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CZAW CH601XLB Zodiac
9
Engine Mount
9.1
Loads on engine mount
Load Analysis
Each of the following two conditions must be investigated: A. Limit torque + positive maneuvering flight load CSVLA A9 (d)(2) Maximum torque at takeoff power:
M eng = 121Nm
CSVLA 361 (b)(1)(ii) Limit torque for 4stroke/4cylinder:
M lim = 2.0 ⋅ M eng = 242 Nm
Limit loads resulting from the maximum positive maneuvering flight load factor n1:
Teng ,lim = n1 ⋅ (meng + m prop ) ⋅ g Teng ,lim = n ⋅ (65kg + 12kg ) ⋅ 9.806 = 2'870 N Ultimate load in vertical direction:
Teng ,ult = 1.5 ⋅ Teng ,lim = 4'305 N
B. Lateral (side) limit load CSVLA A9 (d)(3) Lateral (side) limit load:
Teng ,lat lim = 1,47 ⋅ (meng + m prop ) ⋅ g Teng ,lat lim = 1,47 ⋅ (65kg + 12kg ) ⋅ 9.806 = 1'110 N
Ultimate load in lateral direction:
Teng ,lat ,ult = 1.5 ⋅ Teng ,lat lim = 1'665 N
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10
CZAW CH601XLB Zodiac
Load Analysis
Ground Loads
The requirements for ground loads are specified in CSVLA 471 – 499. CSVLA 473 (b) Descent velocity:
1
vvertical
m ⋅ g = 0.51 ⋅ MTOW S Wing
vvertical
m 600kg ⋅ 9.806 2 s = 0.51 ⋅ 2 12.3m
4
1
4
= 2.39
m s
CSVLA 473 (c) Remaining wing lift at landing impact: LT / D =
2 2 ⋅ Ltotal = ⋅ 600kg ⋅ 9,806 = 3'922 N 3 3
ASTM F224504 5.8.1.1 The load factor nj on the wheels for the basic landing conditions can be computed according to ASTMrequirements:
m⋅g 600kg ⋅ 9.806 = 0.0132 = 28.9cm S 12.3m 2
Drop height:
hdrop = 0.0132
Total shock absorber travel:
d = d tire + d shock = 8 + 18 = 26cm 3
Shock efficiency:
R = 0 .5
for tire and spring shocks
d 26 28.9 + 3 = 3 = 2.89 R⋅d 0.5 ⋅ 26
hdrop + Load factor on the wheels:
nj =
Limit landing load factor:
n = n j + L = 2.89 +
2 = 3.56