airplane performance & design

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/* ------------------------------------------------ -------------------- PROGRAM: index.html Ver: 1.0 Re v: 03/01/2010 DESCRIPTION: www.neatinfo.com main menu BY: Jan Zumwalt - www.zoomaviation.com ------------------------------------------------ -------------------- COMMENTS: Practical calculation of aircraft p erformance Compiled and ran on the free Pellec C compiler http://www.smorgasbordet.com/pelles c/ ------------------------------------------------ -------------------- Ver info: V1.0 users will note slight variations in output compared to the basic version of this program due to different ro und off error in math packages. */ #include <stdio.h> #include <math.h> /* ------------------------------------------------ -------------------- This section is user variables that can be custo mized to a particular aircraft. See The book for descriptions. ------------------------------------------------ -------------------- */ const float altitude_ft = 0.00; // Defines the value of Pi as fixed const float air_density_slug = 0.00237; // (sealevel) const float pi = 3.14159; // Defines the value of Pi as fixed const float vel_delta = 1.00; // airspeed increment for each iteration const float vel_stall_clean_mph = 67.00; // VS1 const float cl_max_clean = 1.53; // const float cl_max_flap = 2.10; // const float gross_lb = 1500.00; // const float useful_load_lb = 600.00; // const float plane_efficiancy = 0.744; // const float bhp = 150.00; // Defines the value of Pi as fixed const float vel_max_mph = 180.00; // const float prop_dia_in = 72.00; // const float prop_dia_ft = 72 / 12; // const float wing_span_ft = 20.83; // const float prop_max_rpm = 2700.00; // // end of user editable custom variables void main() float wing_load_lb_ft = cl_max_clean * po w(vel_stall_clean_mph,2) / 391; // float vel_stall_flaps_mph = sqrt(wing_load_lb _ft * 391 / cl_max_flap); // VS0 float wing_area_ft = gross_lb / wing_l oad_lb_ft; // float wing_aspect = pow(wing_span_ft, 2) / wing_area_ft; // float wing_chord_ft = wing_span_ft / wi ng_aspect; // float wing_span_effective = wing_span_ft * sq rt(plane_efficiancy); // float wing_chord_effective = wing_area_ft / wi ng_span_effective; // float wing_load_effective = gross_lb / wing_s pan_effective; // float drag_area_ft = .8 * bhp * 146625 / pow(vel_max_mph,3); // // float cd_drag = drag_area_ft / wi ng_area_ft; // float vel_sink_min_ft = 11.29 * sqrt(wing _load_effective) / sqrt(sqrt(drag_area_ft)); // float pwr_min_req_hp = .03922 * sqrt( sq rt(drag_area_ft)) * wing_load_effective * sqrt(wing_load_effective); // float rate_sink_min_ft = 33000 * pwr_min_r eq_hp / gross_lb; // float ld_max = .8862 * wing_span _effective / sqrt(drag_area_ft); //

float drag_min = gross_lb / ld_max ; // float cl_min_sink = 3.07 * sqrt(drag_ area_ft) / wing_chord_effective; // float rate_climb_ideal = 33000 * bhp / gro ss_lb; // float prop_tip_mach = prop_max_rpm * pr op_dia_ft * .05236 / 1100; // float prop_vel_ref = 41.9 * pow(bhp / pow(prop_dia_ft,2),.33333); // float static_thrust_ideal = 10.41 * pow(bhp * prop_dia_ft,.66666); // printf("\n\t wing_load_lb_ft = %.02f", wing _load_lb_ft); printf("\n\t vel_stall_flaps_mph = %.02f", vel_ stall_flaps_mph); printf("\n\t wing_area_ft = %.02f", wing _area_ft); printf("\n\t wing_aspect = %.02f", wing _aspect); printf("\n\t wing_chord_ft = %.02f", wing _chord_ft); printf("\n\t wing_span_effective = %.02f", wing _span_effective); printf("\n\t wing_chord_effective = %.02f", wing _chord_effective); printf("\n\t wing_load_effective = %.02f", wing _load_effective); printf("\n\t drag_area_ft = %.02f", drag _area_ft); printf("\n\t cd_drag = %.04f", cd_d rag); printf("\n\t vel_sink_min_ft = %.02f", vel_ sink_min_ft); printf("\n\t pwr_min_req_hp = %.02f", pwr_ min_req_hp); printf("\n\t rate_sink_min_ft = %.02f", rate _sink_min_ft); printf("\n\t ld_max = %.02f", ld_m ax); printf("\n\t drag_min = %.02f", drag _min); printf("\n\t cl_min_sink = %.02f", cl_m in_sink); printf("\n\t rate_climb_ideal = %.02f", rate _climb_ideal); printf("\n\t prop_tip_mach = %.02f", prop _tip_mach); printf("\n\t prop_vel_ref = %.02f", prop _vel_ref); printf("\n\t static_thrust_ideal = %.02f", stat ic_thrust_ideal); printf("\n\n"); printf("\n\t ----------------------------------- ------------------------------------------"); printf("\n\t airspeed \t climb rate \t prop eff \t sink rate \t rennolds num"); printf("\n\t v(mph) \t rc(fpm) \t eta \ t rs(fpm) \t re=rho*v*c/mu"); printf("\n\t ----------------------------------- ------------------------------------------"); float eta = 1; float fp = 0; float rc = 1; float rc1 = 0; float rc2 = 0; float rcmax = 0; float rec = 0; float rsh = 0; float rmu = 1; float rs = 0; float sig = pow(1 - altitude_ft / 145800,4.265); // float t = 518.7 - 0.00356 * altitude_ft; float t1 = .3333; float t2 = 0; float v = vel_stall_clean_mph; float vh = 0; float vmax = 0; float vt = 0; float wv2 = 0; while (rc > 0) vh = v / vel_sink_min_ft; rsh = .25 * (pow(vh,4) + 3) / vh; rs = rsh * rate_sink_min_ft; vt = v / prop_vel_ref; t2 = sqrt(1 + .23271 * pow(vt,3)); eta = .92264 * vt * (pow( 1 + t2,t1) - pow(t2 - 1,t1)) * .85; rc = rate_climb_ideal * eta - rs;

rc2 = rc; rec = sig * v * wing_chord_ft * 9324 / rmu; if (rc < 0) break; rcmax = fmax(rc,rcmax); vmax = fmax(v,vmax); printf("\n\t %.01f \t %.01f \t %.02f \t %.01f \t %.0f",v, rc, eta, rs, rec ); v = v + vel_delta * rc2 / (rc2 - rc1); fp = rcmax * useful_load_lb / 33000 / bhp * (1 - (vel_stall_flaps_mph / vmax)); wv2 = gross_lb * pow(v,2); printf("\n\n\t performance parameter......... f p = %.04f",fp); printf("\n\t kinetic energy parameter...... wv2 = %.02f",wv2); printf("\n\t maximum rate of climb.. ...... rcm ax = %.02f",rcmax); printf("\n\t maximum speed................. vma x = %.02f",vmax); printf("\n\t useful load lb....... useful_load_ lb = %.02f",useful_load_lb); printf("\n\n\t +-------------------------------- ----------------------+"); printf("\n\t | Thank you for us ing |"); printf("\n\t | Air-Performance 1.0 |"); printf("\n\t +---------------------------------- --------------------+"); printf("\n\n\t Press <Enter> key to exit... "); while ((getchar()) != '\n'); printf("\n");

OUTPUT... ------------------------------------------------- ---------------------------- airspeed climb rate prop eff sink rate re nnolds num v(mph) rc(fpm) eta rs(fpm) re= rho*v*c/mu ------------------------------------------------- ---------------------------- 67.0 1175.5 0.63 896.1 256 1031 68.0 1196.3 0.63 891.1 259 9255 69.0 1216.2 0.64 886.6 263 7480 70.0 1235.3 0.64 882.6 267 5704 71.0 1253.5 0.65 879.1 271 3928 72.0 1271.0 0.65 876.1 275 2153 - - - 170.0 183.4 0.82 2521.4 649 8138 171.0 147.3 0.82 2559.0 653 6362 172.0 110.7 0.82 2597.2 657 4587 173.0 73.5 0.82 2635.9 6612 811 174.0 35.8 0.82 2675.0 6651 035 performance parameter......... fp = 0.1206 kinetic energy parameter...... wv2 = 45937500. 00 maximum rate of climb.. ...... rcmax = 1482.42 maximum speed................. vmax = 174.00 useful load lb....... useful_load_lb = 600.00 +------------------------------------------------ ------+ | Thank you for using | | Air-Performance 1.0 | +------------------------------------------------ ------+ Press <Enter> key to exit...

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Appendix A

(information not in the original book)

Appendix B

(information not in the original book)

Aviation Math Symbols

Α, α Alpha angle Β, β Beta Γ, γ Gamma

∆, δ Delta change or press/ratio Ε, ε Epsilon Ζ, ζ Zeta Η, η Eta Θ, θ Theta temp/ratio Ι, ι Iota Κ, κ Kappa Λ, λ Lambda Μ, µ Mu Ν, ν Nu Ξ, ξ Xi

Ο, ο Omicron Π, π Pi 3.141 Ρ, ρ Rho density Σ, σ Sigma density/ratio Τ, τ Tau Υ, υ Upsilon Φ, φ Phi trig angle, i.e. sin, cos Χ, χ Chi Ψ, ψ Psi Ω, ω Omega ∠ angle ° degree ≅ approximate ≤ less than or equal ≥ more than or equal

± plus or minus ∞ infinity ∑ sum oC = ( oF-32) * 5/9 oF = ( oC * 5/9) + 32 oR = oF + 460 oK = oC + 273 ft/min = mph * 88 ft/sec = kt * 1.69 ft/sec = mph * 1.47 kt = mph * 0.87

kt = 69.1

fps

mph = kt * 1.15 Note: unit of measure may be in subscript. For example, a distance (X) may be given as Xft or Xin . a = acceleration AC = aerodynamic center AR = wing aspect ratio (no dim) b = wing span C = chord CF = coefficient of force (no dim) CG = center of gravity CL = coefficient of lift (no dim) CLmax = max C L (no dim)

d = distance D = drag Dmin = minimum drag Di = induced drag Dp = parasite drag Dt = total drag EAS = equivalent air speed F = force Fb = braking force FR = friction ft = feet ft/m = feet per minute ft/s = feet per second G = gravity – 32.2(ft/s 2) H = head (total pressure) h = height hp = horse power IAS = indicated air speed k = constant KE = kinetic energy kt = knot L = lift L/D = lift to drag ratio (no dim) L/D max = max lift/drag ratio (no dim) m = mass MAC = mean aerodynamic chord mph = mile per hour N = weight on wheels ŋ = efficiency ŋP = propulsive efficiency P = air density(slugs) PA = power available PE = potential energy PR = power required q = dynamic pressure RN = renold number ROC = rate of climb S = surface area sl = slug SL = sea level Ŧ = thrust (lb) t = time ŦA = thrust available TAS = true air speed TE = total energy ŦR = thrust required u = friction coefficient (no dim) V = velocity VS = velocity at stall VX = velocity best angle VY = velocity best ROC W = weight X = distance or unknown Y = height or unknown

δδδδ = )(P

)(

SL hg

hgP

θθθθ = °

°T

T SL

σσσσ = SLδδ

* θ = SLδδ

*°

°T

T SL

q = 295

)(2 ktsV∗σ

a(fps 2) = )(2.32/)(

)(

glbW

lbF

= )(

)(

sgm

lbF

= )(*2

)()( 22

ftd

fpsVfpsV endstart +

= [ ])()()(*)(

)(2.32lbFlbDlbT

lbW

gR−−

AR = )(meanchord

span =

area

span2

CAS = IAS ± ∆V”chart”

CL = )(*)(*)(*2/1

)(22 ftSfpsVsgp

lbL

CL = )()(

)(29522 ftSktV

lbw

∗∗∗

σ

d(ft) = V av(fps) * t(s)

= 2

)()( fpsVfpsV endstart + * t(s)

dtakeoff (ft) = [ ]

)(*2

)()(2

2

fpsa

fpswindfpsVTakeoff ±

d2_takeoff (ft) =

2

1

2_1 )(

)(*)(

lbW

lbWftd takeoff

=

2

2

1_1 *)(

σσ

ftd takeoff

d land (ft) = [ ]

)(*2

)()(2

2

fpsa

fpswindfpsVTakeoff ±

d2_land (ft) =

)(

)(*)(

1

2_1 lbW

lbWftd Land

=

2

_1_1 )(

)(1*)(

+

fpsV

fpswindftd

landLand

=

2

1_1 *)(

σσ

ftd land

DT(lb) = ½*p(alt)*V 2(fps)*S(ft 2)*C d

Di min = drag induced at (L/D)max(lb)

DP = 2

1

2min *2

V

VD

Di = 2

2

1min *2

V

VD

Dt = D p + D i

Dmin = max)/(

)(

DL

lbW

EAS = CAS ± ∆V”chart Fb = u * N

hp = 325

)(*)( ktVlbT

m(sg) = )(32

)(

fps

lbW

Vs(fps) = )(*)(*

)(22

max ftSaltpC

lbW

L

∗

TAS = EAS * density = σ1

IASV

Vtip (fps) = 55.9

*)( rpmftr

VDIST = )(*)(*2 2 ftdfpsa

VDmin = )(**

)(2952ftSC

lbW

L σ∗

S(ft 2) = )()(

)(*)(

21

22

lbWlbW

ftLlbW

+

t(s) = )(

)(2fpsa

fpsV

hyp = 22 basalt + =

a

alt

∠sin =

b

alt

∠cos

= a

base

∠cos =

b

base

∠sin

alt = 22 bashyp + =

a

bas

∠tan

= b

bas

∠tan = hyp * Sin ∠α

bas = hyp * Cos ∠α = b

alt

∠tan

= alt * tan ∠b = hyp * cos ∠a = hyp * sine ∠b

Tan ∠∠∠∠αααα = bas

alt

∠∠∠∠a = 90 – b

***************************************

A1 = V 1 = P 1 = σ = q1 = A2 = V 2 = P 2 = σ = q2 = A3 = V 3 = P 3 = σ = q3 =

A1*V 1 = A 2*V 2 = A 3*V 3

q1 = ½ * P * V 12 =

295

)(21 ktsV∗σ

H = P 1 + q 1

V2(kt) = )(

)()(2

2

12

1

ftA

ktVftA ∗

q2 = 295

)(22 ktsV∗σ

p2 = H - q 2

A3(ft 2) = )(

)()(

3

22

2

ktV

ktVftA ∗

q3 = 295

)(23 ktsV∗σ

p3 = H – q 3

CG(ft) = ∑

∑)(

)/(

lbW

lbftMom

= [ ]

[ ]∑∑

)(

)(*)(

lbW

ftArmlbW

************************************

Appendix C

(information not in the original book)

Design Notes

Appendix D

(information not in the original book)

Graphs & Charts

Log Paper