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/* -------------------------------------------------------------------PROGRAM: index.html Ver: 1.0 Rev: 03/01/2010 DESCRIPTION: www.neatinfo.com main menu BY: Jan Zumwalt - www.zoomaviation.com -------------------------------------------------------------------COMMENTS: Practical calculation of aircraft performance Compiled and ran on the free Pellec C compiler http://www.smorgasbordet.com/pellesc/ -------------------------------------------------------------------Ver info: V1.0 s will note slight variations in output compared to the basic version of this program due to different round off error in math packages. */ #include <stdio.h> #include <math.h> /* -------------------------------------------------------------------This section is variables that can be customized to a particular aircraft. See The book for descriptions. -------------------------------------------------------------------*/ const float altitude_ft const float air_density_slug const float pi const float vel_delta const float vel_stall_clean_mph const float cl_max_clean const float cl_max_flap const float gross_lb const float useful_load_lb const float plane_efficiancy const float bhp const float vel_max_mph const float prop_dia_in const float prop_dia_ft const float wing_span_ft const float prop_max_rpm // end of editable custom void main() { float wing_load_lb_ft = float vel_stall_flaps_mph = float wing_area_ft = float wing_aspect = float wing_chord_ft = float wing_span_effective = float wing_chord_effective = float wing_load_effective = float drag_area_ft = // float cd_drag = float vel_sink_min_ft = sqrt(sqrt(drag_area_ft)); // float pwr_min_req_hp = sqrt(wing_load_effective); // float rate_sink_min_ft = float ld_max =

= 0.00; = 0.00237; = 3.14159; = 1.00; = 67.00; = 1.53; = 2.10; = 1500.00; = 600.00; = 0.744; = 150.00; = 180.00; = 72.00; = 72 / 12; = 20.83; = 2700.00; variables

// // // // // // // // // // // // // // // //

Defines the value of Pi as fixed (sealevel) Defines the value of Pi as fixed airspeed increment for each iteration VS1

Defines the value of Pi as fixed

cl_max_clean * pow(vel_stall_clean_mph,2) / 391; sqrt(wing_load_lb_ft * 391 / cl_max_flap); gross_lb / wing_load_lb_ft; pow(wing_span_ft,2) / wing_area_ft; wing_span_ft / wing_aspect; wing_span_ft * sqrt(plane_efficiancy); wing_area_ft / wing_span_effective; gross_lb / wing_span_effective; .8 * bhp * 146625 / pow(vel_max_mph,3);

// // VS0 // // // // // // //

drag_area_ft / wing_area_ft; 11.29 * sqrt(wing_load_effective) /

//

.03922 * sqrt( sqrt(drag_area_ft)) * wing_load_effective * 33000 * pwr_min_req_hp / gross_lb; .8862 * wing_span_effective / sqrt(drag_area_ft);

// //

float float float float float float

drag_min cl_min_sink rate_climb_ideal prop_tip_mach prop_vel_ref static_thrust_ideal

printf("\n\t printf("\n\t printf("\n\t printf("\n\t printf("\n\t printf("\n\t printf("\n\t printf("\n\t printf("\n\t printf("\n\t printf("\n\t printf("\n\t printf("\n\t printf("\n\t printf("\n\t printf("\n\t printf("\n\t printf("\n\t printf("\n\t printf("\n\t

= = = = = =

gross_lb / ld_max; 3.07 * sqrt(drag_area_ft) / wing_chord_effective; 33000 * bhp / gross_lb; prop_max_rpm * prop_dia_ft * .05236 / 1100; 41.9 * pow(bhp / pow(prop_dia_ft,2),.33333); 10.41 * pow(bhp * prop_dia_ft,.66666);

wing_load_lb_ft vel_stall_flaps_mph wing_area_ft wing_aspect wing_chord_ft wing_span_effective wing_chord_effective wing_load_effective drag_area_ft cd_drag vel_sink_min_ft pwr_min_req_hp rate_sink_min_ft ld_max drag_min cl_min_sink rate_climb_ideal prop_tip_mach prop_vel_ref static_thrust_ideal

= = = = = = = = = = = = = = = = = = = =

%.02f", %.02f", %.02f", %.02f", %.02f", %.02f", %.02f", %.02f", %.02f", %.04f", %.02f", %.02f", %.02f", %.02f", %.02f", %.02f", %.02f", %.02f", %.02f", %.02f",

// // // // // //

wing_load_lb_ft); vel_stall_flaps_mph); wing_area_ft); wing_aspect); wing_chord_ft); wing_span_effective); wing_chord_effective); wing_load_effective); drag_area_ft); cd_drag); vel_sink_min_ft); pwr_min_req_hp); rate_sink_min_ft); ld_max); drag_min); cl_min_sink); rate_climb_ideal); prop_tip_mach); prop_vel_ref); static_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 float fp float rc float rc1 float rc2 float rcmax float rec float rsh float rmu float rs float sig // float t float t1 float t2 float v float vh float vmax float vt float wv2 while (rc { vh rsh rs vt t2 eta rc

= = = = = = = = = = = = = = = = = =

1; 0; 1; 0; 0; 0; 0; 0; 1; 0; pow(1 - altitude_ft / 145800,4.265); = 518.7 - 0.00356 * altitude_ft; .3333; 0; vel_stall_clean_mph; 0; 0; 0; 0;

> 0) = = = = = = =

v / vel_sink_min_ft; .25 * (pow(vh,4) + 3) / vh; rsh * rate_sink_min_ft; v / prop_vel_ref; sqrt(1 + .23271 * pow(vt,3)); .92264 * vt * (pow( 1 + t2,t1) - pow(t2 - 1,t1)) * .85; 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 rec ); v = v + vel_delta * rc2 / (rc2 - rc1); } fp

\t

%.01f

\t

%.0f",v, rc, eta, rs,

= rcmax * useful_load_lb / 33000 / bhp * (1 - (vel_stall_flaps_mph / vmax));

wv2

= gross_lb * pow(v,2);

printf("\n\n\t performance parameter......... fp printf("\n\t kinetic energy parameter...... wv2 printf("\n\t maximum rate of climb.. ...... rcmax printf("\n\t maximum speed................. vmax printf("\n\t useful load lb....... useful_load_lb

= = = =

= %.04f",fp); %.02f",wv2); %.02f",rcmax); %.02f",vmax); %.02f",useful_load_lb);

printf("\n\n\t +------------------------------------------------------+"); printf("\n\t | Thank you for using |"); 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 rennolds num v(mph) rc(fpm) eta rs(fpm) re=rho*v*c/mu ----------------------------------------------------------------------------67.0 1175.5 0.63 896.1 2561031 68.0 1196.3 0.63 891.1 2599255 69.0 1216.2 0.64 886.6 2637480 70.0 1235.3 0.64 882.6 2675704 71.0 1253.5 0.65 879.1 2713928 72.0 1271.0 0.65 876.1 2752153 170.0 183.4 0.82 2521.4 6498138 171.0 147.3 0.82 2559.0 6536362 172.0 110.7 0.82 2597.2 6574587 173.0 73.5 0.82 2635.9 6612811 174.0 35.8 0.82 2675.0 6651035 performance parameter......... fp kinetic energy parameter...... wv2 maximum rate of climb.. ...... rcmax maximum speed................. vmax useful load lb....... useful_load_lb

= = = = =

0.1206 45937500.00 1482.42 174.00 600.00

+------------------------------------------------------+ | 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 Β, β Γ, γ ∆, δ Ε, ε Ζ, ζ Η, η Θ, θ Ι, ι Κ, κ Λ, λ Μ, µ Ν, ν Ξ, ξ Ο, ο Π, π Ρ, ρ Σ, σ Τ, τ Υ, υ Φ, φ Χ, χ Ψ, ψ Ω, ω ∠ ° ≅ ≤ ≥ ± ∞ ∑ o

C F o R o K o

angle Beta Gamma Delta change or press/ratio Epsilon Zeta Eta Theta temp/ratio Iota Kappa Lambda Mu Nu Xi Omicron Pi 3.141 Rho density Sigma density/ratio Tau Upsilon Phi trig angle, i.e. sin, cos Chi Psi Omega

angle degree approximate less than or equal more than or equal plus or minus infinity sum = = = =

(oF-32) * 5/9 (oC * 5/9) + 32 o F + 460 o C + 273

ft/min = mph * 88 ft/sec = kt * 1.69 ft/sec = mph * 1.47 kt = mph * 0.87 kt = fps 1.69

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 = AC = AR = b = C = CF CG = CL CLmax

acceleration aerodynamic center wing aspect ratio (no dim) wing span chord = coefficient of force (no dim) center of gravity = coefficient of lift (no dim) = max CL (no dim)

d = D = Dmin = Di = Dp = Dt = EAS = F = Fb = FR = ft = ft/m ft/s G = H = h = hp = IAS = k = KE = kt = L = L/D = L/Dmax m = MAC = mph = N = ŋ = ŋP = P = PA = PE = PR = q = RN = ROC = S = sl = SL = Ŧ = t = ŦA = TAS = TE = ŦR = u = V = VS = VX = VY = W = X = Y =

distance drag minimum drag induced drag parasite drag total drag equivalent air speed force braking force friction feet = feet per minute = feet per second gravity – 32.2(ft/s2) head (total pressure) height horse power indicated air speed constant kinetic energy knot lift lift to drag ratio (no dim) = max lift/drag ratio (no dim) mass mean aerodynamic chord mile per hour weight on wheels efficiency propulsive efficiency air density(slugs) power available potential energy power required dynamic pressure renold number rate of climb surface area slug sea level thrust (lb) time thrust available true air speed total energy thrust required friction coefficient (no dim) velocity velocity at stall velocity best angle velocity best ROC weight distance or unknown height or unknown

δ =

P(hg ) PSL (hg )

θ =

T ° SL T°

σ =

δ δ SL

* θ =

δ T ° SL * δ SL T °

DT(lb) = ½*p(alt)*V2(fps)*S(ft2)*Cd

σ ∗ V 2 (kts )

q =

a(fps2) =

=

Dimin = drag induced at (L/D)max(lb)

295 F (lb) W (lb) / 32.2( g )

F (lb) m( sg )

2

  Di = D min *  V 1 

2

2

Vstart ( fps ) + Vend ( fps ) = 2 * d ( ft ) 32.2( g ) = * [T (lb) − D(lb) − FR (lb)] W (lb) 2

AR =

  DP = D min *  V 2  2  V1 

2

Dt = Dp + Di

W (lb) ( L / D ) max

Dmin =

span span 2 = chord (mean) area

EAS = CAS ± ∆V”chart Fb = u * N

CAS = IAS ± ∆V”chart” hp = CL =

L (lb) 1 / 2 * p ( sg ) * V 2 ( fps ) * S ( ft 2 )

T (lb) * V (kt ) 325 W (lb) 32( fps )

m(sg) = CL =

V 2 

295 ∗ w(lb) σ ∗ V 2 (kt ) ∗ S ( ft 2 )

Vs(fps) =

C L max

d(ft) = Vav(fps) * t(s)

=

Vstart ( fps ) + Vend ( fps ) * t(s) 2 2 VTakeoff ( fps ) ± wind ( fps )

[

dtakeoff(ft) =

Vtip(fps) =

W (lb)  d2_takeoff(ft) = d 1 _ takeoff ( ft ) *  2   W1 (lb)  σ  = d 1 _ takeoff ( ft ) *  1  σ 2 

dland(ft) =

d2_land(ft) =

[V

Takeoff

2

( fps ) ± wind ( fps )

]

2

VDIST =

2 * a( fps 2 ) * d ( ft )

VDmin =

295 ∗ W (lb) C L * σ * S ( ft 2 )

2

2 * a ( fps )

W (lb)  d1 _ Land ( ft ) *  2   W1 (lb) 

σ  d1 _ land ( ft ) *  1  σ 2 

2

VIAS

r ( ft ) * rpm 9.55

2

 wind ( fps )  = d1 _ Land ( ft ) * 1 +   V1 _ land ( fps ) 

=

TAS = EAS * density =

]

2 * a( fps 2 )

2 ∗ W (lb) * p (alt ) * S ( ft 2 )

S(ft2) =

t(s) =

W2 (lb) * L2 ( ft ) W1 (lb) + W2 (lb)

V ( fps ) a ( fps 2 )

1

σ

hyp =

=

alt + bas 2

2

alt alt = = sin ∠a cos ∠b

base base = cos ∠a sin ∠b

alt =

=

q1

=

½ * P * V12

H

=

=

A3*V3 =

σ ∗ V1 2 (kts) 295

P1 + q1

A1 ( ft 2 ) ∗ V1 (kt ) V2(kt) = A2 ( ft 2 ) σ ∗V 2 2 (kts) 295

A3(ft2) =

alt tan ∠b

q3 =

A2 ( ft 2 ) ∗ V2 (kt ) V3 (kt )

σ ∗V3 2 (kts)

= alt * tan ∠b = hyp * cos ∠a

295

p3 = H – q3

= hyp * sine ∠b Tan ∠α =

A2*V2

p2 = H - q2

bas tan ∠a

= hyp * Sin ∠α

bas = hyp * Cos ∠α

=

q2 =

hyp 2 + bas 2 =

bas = tan ∠b

A1*V1

alt bas

∠a = 90 – b ***************************************

CG(ft)

=

=

A1 = V1 = P1 = σ = A2 = V2 = P2 = σ = A3 = V3 = P3 =

q1 = q2 = σ =

∑ Mom( ft / lb) ∑W (lb)

∑ [W (lb) * Arm( ft )] ∑ [W (lb)]

************************************ q3 =

Appendix C (information not in the original book)

Design Notes

Appendix D (information not in the original book)

Graphs & Charts

Log Paper