Chapter VISample design and performance estimate

Landing speed and wing area ,a<

the Zenair series is ao examDle oi ciassic metal monocoque construction.

The Zenith CH 200

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' l his cl)aptcf describcs a si lrple nlethod lbr the design ol a l ighl shcet lnetAl alrplanc 01

con!enti;nrl corl iSurlt ion. ' Ihis task is. lone easily u' i th some shccts of paPef a pcncrl '

rnd a eraser ( lbf correcl ions), plus a cheap pocket calcula()r ' Thcre is no need Jit r

compuler. wcb l inks, splead sheels, etc

' lhe Super Zodiac Cl l 6() I HDS 11992).

222

The Zenith' l inni ly'r Cll { l 50..Aclo Zenith. C H 200 Zenith and CH 300 Tli Zenith

Basic choices and weightThe airplane is intended to cany the occupants (pilot plus passenger(s)) and the fuelrequircd to ke€p the engine running for at least the length of time we want to enjoy flying.The weight of each occupant is estimated at 90 kg (= 200 lbs) and the fuel consimptron at. 2 kg/BHP x hrs. For an 80 BHp engine and 3 hours of endurance we neerl:

. 2 x 80 x 3 = 48 kg = 50 kg otfuel

The total useful load for our 2 seat airplane:Wu=2x90f50=230kg

If we want to cany baggage or ifthe occupants are heavier (which seems to be ,.normal,,today, thanks to "junk food" atd little physical exercise), we have to adjust the aboveuseful load.

Careful when selecting the engine: Never design a new airylane to be powered with anunknown engine: The potential problems will be doubled, and our .,fantastic,, desrgn maybecome a failure because ofan unreliable engine... or vice versa!

Alsocarefully check the powerplant weight (engine +exhaust+ cooling liquid +rcductrongear + propeller + other accessodes). ls your engine within acceptable limits of today,stechnology (less than I kg per horse power)? Check also the fuel consumption: does it fitthe above assumption?

Now we will estimate the empty weight by choosing one of the columns from the table below:

This corresponds to501.'72 ='70litets = l9 US gallons ofusable fuel.

column I A very basic light airplane,

We = empty weightWu = useful loadW = Maximum airplane weight

column 2 and 3 A simple airplane and straight forward design.c,' lumn 4 A elassic airplane mrrderarelS simple to buiid,column 5 and 6 Either a single seater or a very strong (acrobatic?) airplane with heavy

equipment, good fairings and certain design comprcmises for easy manufacnr ng.

t234

We/Wu .8 | .0 t.Z | .4 2.0

3.0w/WU 1.8 2.0 2.2 2.4

Y* ra 5 r ' * LE Y

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This provides us with quite a wide range! L-et us not overestrmate our capabilities'

especially if this is our iirst attempt at designing an airplane Unless we arc a genlus'

ou'r airplane wilt most likely end up heavier than anticipated on the scales So' let us be

humble when determining the Maximum weight:

w=we+wu=wu(.q,€r1)\wu I

For our example, we modestly assume we arc just an adequate designer and chose column

4 to obtain our Maximum weight:

W = 230 (14 r 1) -

550 kg

Manufacturing "Quick built" kits

2U

Landing speed and wing areaAfter having chosen the weights, we now select the ma,rimum stall speeds:

Vso = 72 km/h = 45 mph = 39 kts (flaps down)Vs = 8l km/h = 50 mph = 44 kts (flaps up)

With these speeds, the airplane will be easy to land, which is one of the purposes of thistype of airplane. lf you just design another .,ex perimental', airplan", you

"un io up t , V.o= 60 mph, but remember that near and above this speed, the energy becomes"so large thatthere is l i t t le chance ofsurvival intheeventofalandingaccident(seep.2l6).

Now weneed to know the ailplane'smaximum liftcoefficientClM* lbr both configuratbns:flaps down and flaps up. This depends on the wing plan forfr, fhe airfoil cioice. thecenter of gravity (C.G.) position, etc. Without going into complicated theories and basedon our geneml goals for this simple airplane, we estimate and choose an airfoil from aconfiguration below. Clr* applies to full span flaps.

&fiot', ' t

t46a " 2"L

ek*t'2,8 ekt;ft"( {@

Clt*" 1,/ 9la ta "*rt

For a.simple design we choose a simple plain flap and do not forget that the flap span otthe wing is only about 14 the wing spam (the ailerons occupy the outboard part):

t . -5 .2.221

j " '=|ct noCl ,". flaps down

Cl",* flaps up

flaps + plain flaps l 85

225

With these values' we determtne the required wing area S to meet the selected stall speed

requ1rements:

W=qClM", Swithq=:

) = -tar"_

For the clean (flaps uP) airplane:^-- 'V=8!km/h q=32kg/m2

v in km/hWinkgslnm-

because q = \tt4,J

*=(f) ' " tsr . '

q- 550 =l l46m?" 32x15

And with flaps extended:

V = 72 knr.rh q = 25 kg/ml

g = rJ!!-

= 11.9n1'

We choose a wing area of 12 mr and thus meet oxr stall speed requtremenls'

Now we have to make morc choices:. High or low wing?. Tricvcle or taildragger gear'/. Tractor or Pusher Power?lant?. Open or enclosed cabin?

Your imagination is the limit The less you have attended college and/or universlty' the

more creative you probably still arel

But keep in mind that unless you are desiening this wonderful new airplane tust ror

vourself. it needs to b" tuth"t "onu"ntto*l

it you wxnt others to tl) it t)r hope to sell it to

'o* ir"aii"""t nt'* "ommunity

which is very consewative'

l wish l coulci remember or find the author ofthis quote as 1 fully aglee with it:

We know the old: It is warmer and familiar'It is also compulsory and fragile'

It is worn out!

We fear the new: lt is cooler and strange'But it is more free and sffonger'

It is Youthful!

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Performance estimat€sFull throttle, sea leyel speed, for a well faired and comfortabiewith an efficient propeller is close to:

side by side two seater

v,, = r50 .,@" v s+l

= rso l@Yi2+8

= 238 km/h

Note: you can inte4'olate from the fbtbwing table to calculate the cubic root il vourinexprensive calculator only supplies the square rcot:

2 ).5 .r J.5 4 4.5 5 5.5 br26135114l r5rlr 5e r.5s r{ rofr:z

in km,4r with S in m2

= l5o jV-4{) = l5o x r.59

= 147 mph = 128 kts

. -

The ordinary 757o power setting ciuise specd will be .9 x V! = .9 x 23g = 214 km,4r at sealevel. The cruise speed will increase to .95 x Vrr = 225 km/h at an altitude of 6 to 8,000 ftwhere, at full throttle, we will have 75% power, Above this altitude. the cruise sDeed willdecrease (unless the engine is equipped wirh a rurbo charger). an,l we will fly very ckrseto the indicated stall spe€d when we reach the airplane's ceiling.

A very simple way of estimating that our airplane has good takc off and climbpe rrrmancc. is l ( ) calculate Yxw " ' t '

5 Btrp l l In l \ ls smal ler lhan 4OU In m.^El]p we wi l i

have acceptable take off and climb performance. For our example we have:

""Y"= + +=458x68=3rr *S; )n:;*t;'ljf;T= .15.8 kg/m, is called the wing loading

= 6.8 His called the power loading

We estimate the rate of climb at sea level according to:

Vz = 26 H= 26 #il = 3.8 m/s = 750 FPM

And the scryice cciling will be close to:

ryS

vw

(W in kg and Vz in m/s)

Zu^, = 950. Vz = 950 x 3.8 : 3600 m = I 1,800 ft (Vz in m./s)

It is quite informative and worthwhile for our understanding, kr vary the BHp (the engiuepower) in above calculations, and compare Vn, V, and Zr*. We may tlen decide to reducethe installed power and save some weight (empty airylane, fuel, ma\ weight W) and somecost. Designing an airplane is a never ending process ofcompromising.

227

Stability and controllability

An airplane must be stable and controllable around all three axis'

Pitch stability We took carefully at the side view and plan view of our new -d€sign

We

"i".." ,fr. ti"g ai."nsions and know the wing area' J = b x MAC = 8,x l-50 = 12 m"

-a,i" "ro*, i". e = b'?ls = 8r/12 = 5.33. Noi we need the size of the horizonttl tail to

obtain adequate pitch stability.

- b,a1^ CP1

(4= bx N'E,tGr----

The lbllowing formtrla, which is a simplification of the much more complicated stabiliq

theory, is quiie accurate for our liSht airplanes (see p l27)'

j3MAC

.- ^- sHT L-. . , ' " S MAC

It gives us the most rcarwad centef of gravity position x*' at which tlre airplane is still stable'

Note that the above formula applies to low wing airplanes For a high wing^arplar

;;.iily .is rh" ro..,tu i' uulid for stabilator plus elevator' as well as for the c

flying horizontal tail

When we position the occupants in our airplane (side view ) and have fun-designing seven

combinati,ons of tail and rear fuselage' we will have a reasonably good idea of where th

*".iC i-"1 will be and we can determine L from our sketches Here the previousl

mentioned ;raser can come in handy!

Of course the ideal is to have the CG at !4! ;n 611qqn1;gutationsr one ligtt pilot onl

then two heavy occtlpants and baggage and all this with' and wirhout fuell Untortrlnate

tfr" ia"u i,jo.i -

iO"ul! We just have to play with the many possibilities '

228

Select one contiguralion where x, is not too lar back, so we save some weight fbr areasonabl) stzei l horizonral rai l tSHr) and where L is the r ight dimensio!,. , i thut th"airplane looks attractive.

Now we calculate the arca ofthe horizontal rail:We assume in our example gxat = :27, = .32 and L = 3 m. This gives us:

s _/h ,a\ S.MAC- \ MAC - " / rJ= (.32 - .11) . !?] LJ = 2.43 m.

37x3

And with the usual aspect ratio AHr = 3 lbr the horizontal tail, we obtain:

U,,=r'tr* x S,n =rt x Z+: = 2.7 m (span)

c_=+=2.1

=.9m(chord)

We check again: ls the rear CC position in the above calculation exceeded in the mostunfhvorable loading condition? lf the answer is ,.no',, we stay witl this tail size. But ifthe answer is "yes", we either need a longer fuselage, L, or a larger tail area, Srn, or acombination of both to obtain a stable ailplane.

we have sufticient pitch control when the erevator is 40 to 507, of the horizontar tailchord and its deflection is t 25 to 30 degrees. (Note that an all moving horizontal tailneeds an "Antiservo ffim tab" to provide the pilot with a good..feel,, and to alkrw him/herto trim the airplane, see p. 128)

We also check that the Forward CG limit of nah MA,C is not exceeded at the mostForward CC position: Il the Foryard CG position is less thal I 52. MAC, there is a goodchance that we will "run out of elevatoi, when landing the airplane. Thjs could imposevery high loads on the nose gear of a tricycle gear airplane. ln the case of a tail dagger,a CG that is too far forward will make the airplane even more unstable during taxltng.and landing in crosswind conditions. AIso the pilot may not be able to react fai't enoughto avord ground loops!.

Yaw and Roll stability:For good roll stability the wings are built wirh dihedral:

6 deg f()r a low winc 'tI deg f,,r a high \,\ in-g J

wil l provide lhe needed i labi l i ly

For yaw stability rhe vertical tail area should be 12 to l5rya ofrhe wing area ( t5% ifthe rcar fuselage has a small rounded section, and l27o if the rear fuselagJ has large flatsides). These percentages may be reduced to 7Vo and loa/o fot an,,alt flying,, rudcier.

229

Controllability in yaw will be adequate (for up to approximately 20 knots of cross wind)

if the ruddcr chord is between 20 and 70olo of the vertical tail chord (fin plus rudder)

and the deflection approximately 20 deg (similar deflections for the all flying rudder will

allow crosswinds of up to 30 kts!).

Correct roll control (for crosswind landings, tight quick turns and gusty weather) will be

achieved with the ailerons over 40 to 5070 of the outboard wing span (the ailerons are

near the wing tip!) and the most efficient ailerons have 16 to 207o ofthe wing chord and

a deflection of 15 to l8 deg.

The flap chord should be 20 to 25olo of the wing chord with deflection of some 30 deg'

to obtain the Cl Max from p.225. Larger flap deflections rnay create a shong wake

turbulence running into the hodzontal tail (the stick and even the airplane may shake!)

Too large deflections may not provide much additional lift' although the drag increases

substaniially allowing steep approaches if the elevator has sufficient authority to allow a

nice rounding offjust before touchdown

Some good news: When the completed airplane is measured and put on the scales' and

when its weight antl CG position are calculated' do not despair when you load it' and the

most forwarJ or most rearward CG exceeds the "sale" limits: simply move the battery! It

is a heavy item which can be located where you need it, to achieve the correct CG of the

airplane.

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The CH 620 a two seat twln