# 飛機性能分析
###### tags: `analysis`

| 2維升力係數 | | 3維升力係數 | | 加高升力裝置 |
|:-------------:|:-------:|:-------------:|:-------:|:-----------------------:|
| $C_{lcruise}$ | $0.9166$ | $C_{Lcruise}$ | $1.1317$ | $1.2754$ |
| $C_{lmaxWto}$ | $2.171$ | $C_{LmaxWto}$ | $2.680$ | $2.8237$ |
## 升力
:::danger
\begin{gather*}
性能分析的面積都用機翼扣除機身處的面積
\\
334.174856-41.72483266(chord*fuselage width)=292.450023ft^2
\end{gather*}
:::
### 升力斜率
我們可以從airfoiltool.com上面取得主翼(DAE-31)&尾翼(NACA0012)的二維升力斜率
* DAE-31

可以得到
\begin{gather*}
C_{l_{\alpha,w}}=(1.535-0.344)/(5-(-5)) = 0.1191\\
\end{gather*}
上面那個沒有考慮後略、漸縮等因素，改用下面那個
* $AR = 10$
* $M = 0.2846$ (但在這個公式下<0.3可以忽略不計M=0)
* $\kappa = 0.1191/2\pi = 0.01896 翼型二維升力斜率C_{l\alpha}與2\pi 的比值$
* $A_{c/2} = 0 degree$ 機翼1/2弦線後略角

\begin{gather*}
C_{L\alpha} = \frac{2\pi AR}{2+\sqrt{\frac{AR^2(1-M)^2}{\kappa^2}(1+\frac{tan^2(A_{c/2})}{(1-M)^2})+4}} = 0.1186
\\\\
C_{L\alpha} = \frac{2\pi *10}{2+\sqrt{\frac{10^2(1-0.2371)^2}{0.01896^2}(1+\frac{tan^2(0)}{(1-0.2371)^2})+4}} = 0.1186
\\\\
C_{L\alpha} = 0.1186
\end{gather*}

* NACA0012

可以得到
\begin{gather*}
C_{l_{\alpha,t}}= (0.359-0)/3= 0.1196\\
\end{gather*}
\begin{gather*}
C_{L\alpha} = \frac{2\pi AR}{2+\sqrt{\frac{AR^2(1-M)^2}{\kappa^2}(1+\frac{tan^2(A_{c/2})}{(1-M)^2})+4}} = 0.1172
\\\\
C_{L\alpha} = \frac{2\pi *1.9}{2+\sqrt{\frac{1.9^2(1-0.2371)^2}{0.01903^2}(1+\frac{tan^2(0)}{(1-0.2371)^2})+4}} = 0.1172
\\\\
C_{L\alpha} = 0.1172
\end{gather*}
### 在巡航功角下的升力斜率
* DAE-31 CL = 0 at alpha = -7.75degree
* NACA0012 CL = 0 at alpha = 0
\begin{gather*}
\\
C_{L,w} = C_{L_{\alpha,w}}(\alpha_{deg}-\alpha_{L=0})
\\
\\
C_{L,w} = C_{L_{\alpha,w}}(\alpha_{1deg}-\alpha_{L=0})
\\\\=0.1186*(1degeree-(-7.75degree))
\\\\= 1.03818
\\\\
C_{L,t} = C_{L_{\alpha,t}}(\alpha_{1deg}-\alpha_{L=0})
\\\\=0.08538*(1degree-(0degree))
\\\\= 0.11724
\end{gather*}

### 升力巡航速度分析
縱軸數據
* $S_{w} = 292.45ft^2$
* $S_{t} = 130.1749ft^2$
* $C_{L,w} = 1.038181719$
* $C_{L,t} = 0.1172392004$
* $\rho (20000ft) = 0.001267slug/ft^3$
\begin{gather*}
L = 0.5\rho V^2(S_{w}C_{L,w}+S_{t}C_{L,t})
\end{gather*}
橫軸馬赫數
聲速以訂定的巡航高度 20000ft為準，溫度為249K
* $V = 246.063 ft/s$
* $\gamma = 1.4$
* $R = 1716$
* $T = 448.2R°$
\begin{gather*}
M=\frac{V}{\alpha}=0.2371
\\\\
\alpha=\sqrt{\gamma RT}=\sqrt{1.4*1716*448.2} = 1037.6684
\end{gather*}

將升力-馬赫關係圖繪出後,在巡航攻角為1°的巡航狀態下,且重量以最大起飛重量(12364.4697lb)做保險考量,飛機需要的速度約為馬赫數 0.22~0.23 ,在之前的任務目標訂定將巡航時的速度訂為 246.063 ft/s, 換算成馬赫數約為 0.2371 (巡航高度20000ft),符合分析的標準。


cruise_temperature= 448.2 ; % R
W=12364.46967; % maximum takeoff weight 12364.46967lb
V = linspace(100,400);
S_w = 292.450023; % wing area (ft^2)
S_t = 130.1749; % horizental tail wing area (ft^2)
C_L_t_cruise = 0.1172392004;
C_L_w_cruise = 1.038181719;
roh = 0.001267; % cruise_density at 20000ft (slug/ft^3)
L = 0.5.*roh.*V.^2.*(S_w*C_L_w_cruise+S_t*C_L_t_cruise);
alpha = sqrt(1.4*1716*cruise_temperature);
M = V/alpha;
plot(M,L);
hold on;
yline(W);
xlabel('Mach number');
ylabel('Lift(lb)')

### 升力與功角分析
訂定巡航功角為1 degree ，為求合理性，我們需要考量再巡航速度下各個功角對升力的情形
* $S_{w} = 292.450023ft^2$
* $S_{t} = 130.1749ft^2$
* $C_{L,w} = 1.038181719$
* $C_{L,t} = 0.1172392004$
* $\rho (20000ft) = 0.001267slug/ft^3$

\begin{gather*}
C_{L,w} = 0.1186*(\alpha - (-7.75))
\\
\\
C_{L,t} = 0.08538*\alpha
\\
\\
L = 0.5\rho V^2(S_{w}C_{L,w}+S_{t}C_{L,t})
\end{gather*}

### 巡航升力分析
飛機在進行飛行時,甚至是巡航時並不會一直保持在我們的預設攻角(1°),因此還需考量到飛機在各個不同攻角需要多少速度才能維持巡航的狀態;抑或是在我們訂定的巡航速度下,需要多大攻角才能維持巡航。

將升力-攻角關係圖繪出,由圖可知,當飛機巡航速度為之前所訂之246.063 (ft/s) 時,且重量以最大起飛重量(12364.4697lb)做保險考量,攻角

**不同攻角下,升力-速度關係圖**


%%
cruise_speed=246.063; % ft/s
cruise_temperature= 448.2 ; % R
W=12364.46967; % maximum takeoff weight (12364.46967lb) (5608.42kg)
V = linspace(0,400);
roh =0.001267; % cruise_density at 20000ft (0.001267slug/ft^3)(0.6531kg/m^3)
S_w = 292.450023; % wing area (292.4500234ft^2) (31.04586m^2)
S_t = 130.1749; % horizental tail wing area (ft^2)
C_L_t_cruise = 0.08538;
C_L_w_cruise = 0.1186493393;
alpha = sqrt(1.4*1716*cruise_temperature);
M = V/alpha;
CD0 =0.03702991401;
K = 0.04207109254;
% at AOA 0~5
for i=1:7
    C_L_w = C_L_w_cruise*(i-2-(-7.75));
    C_L_t = C_L_t_cruise*(i-2-(0));
    L = 0.5.*roh.*V.^2.*(S_w*C_L_w+S_t*C_L_t);
    plot(V,L);
    hold on
end
yline(W);
xline(cruise_speed);
xlabel('velocity(ft/s)');
ylabel('lift(lbf)')
legend('AOA = -1','AOA = 0','AOA = 1','AOA = 2','AOA = 3','AOA = 4','AOA = 5');

可知,若以零攻角為例,我們訂定的巡航速度就不夠使飛機維持巡航狀態,由於其升力不夠;若以攻角1度即可接近維持巡航。

## 阻力
### 阻力係數分析

$K=\frac{1}{\pi*e*AR}=\frac{1}{\pi*0.7566*10}=0.04207$

$C_{D}=C_{D0}+C_{Di}+C_{Dw}$

$C_{D0}=C_{D0,form}+C_{D,friction}$

$C_{Di}=KC_{L}^2 = \frac{C_{L}^2}{\pi AR e}$

$C_{Dw}=$

### 主要CDF
\begin{gather*}
C_{D,F}=C_{F}*FF*\frac{S_{wet}}{S_{ref}}
\end{gather*}
:::info
\begin{gather*}
S_{ref} 統一使用主義參考翼面積
\end{gather*}
:::
- 機翼&尾翼濕面積
* 主翼
* $S_{exposed}$ 機翼實際暴露在空氣中的投影面積
* $S_{exposed} = Wing Area = 334.174856 ft^2$
* $t/c = 0.111(DAE-Airfoil)$ 厚弦比
* $x/c = 0.293(DAE-Airfoil)$ 最厚位置
\begin{gather*}
S_{wet}=S_{exposed}(1.977+0.52\frac{t}{c})
\end{gather*}

\begin{gather*}
S_{wet}=334.174856(1.977+0.52*0.111)= 679.952263ft^2
\end{gather*}
* 尾翼
* 水平尾翼面積$5.93m^2 = 63.83ft^2, S_{exp,HT}=63.83ft^2$
* 垂直尾翼面積$5.23m^2 = 56.2953ft^2, S_{exp,VT}=56.2953ft^2$
* NACA0012
* t/c = 0.12
* x/c = 0.3
\begin{gather*}
S_{wet}=S_{exposed}(1.977+0.52\frac{t}{c})
\\
\\
S_{wet.VT}= 114.8086348ft^2
\\
\\
S_{wet.HT}= 130.174902ft^2
\end{gather*}
- 機身濕面積
* $d_{f} = 2.2m = 7.2178ft$ 機身直徑
* $l_{n} = 3.24m = 10.6299ft$ 機鼻長度
* $l_{f} = 15.1m = 49.5407ft$ 機身長度
* $\lambda=l_{f}/d_{f} = 6.8636$ Fineness Ratio

\begin{gather*}
S_{wet}=\pi d_{f} l_{f}(0.5+0.135\frac{l_{n}}{l_{f}})^{2/3}(1.015+\frac{0.3}{\lambda_{f}^{1.5}})
\\
S_{wet}=\pi*7.2178*49.5407*(0.5+0.135\frac{10.6299}{49.5407})^{2/3}(1.015+\frac{0.3}{6.8636^{1.5}})
\\
\\
S_{wet}= 758.0277353 ft^2
\end{gather*}

- 機翼及尾翼的形狀修正係數(FF)
* $t/c = 0.111$
* $x/c = 0.293$

\begin{gather*}
FF=[1+\frac{0.6}{(x/c)_{m}}(t/c)+100(t/c)^4]
\\
\\
FF=1.2425
\end{gather*}

- 機身的形狀修正係數(FF)(for $Re > 10^5$)
* 我們的$Re = 6,561,431$
* 使用橢圓公式求得機身截面積$A_{max}=40.9171ft^2$
* 機身長度 $l=15.1m=49.5407ft$
\begin{gather*}
FF=(1+\frac{60}{f^3}+\frac{f}{400})
\\
f = \frac{l}{\sqrt{4/\pi A_{max}}}
\\
\\
FF = 1.2027
\end{gather*}

- 平板摩擦阻力係數 Flat-plate Skin-friction Coefficient

\begin{gather*}
C_{F}=\frac{0.455}{(log_{10}Re)^{2.58}(1+0.144M^2)^{0.65}} (Turbulent)
\end{gather*}

* Mach number
$a = \sqrt{\gamma RT}=\sqrt{1.4*1716*448.2}=1037.668386 m/s$
$M = 295.275/1037.668386 = 0.2317$
* $Re = 5,421,866$
\
\begin{gather*}
C_{F}=\frac{0.455}{(log_{10}(5421866))^{2.58}(1+0.144*0.2317^2)^{0.65}}
\\
\\
C_{F}= 0.003302
\end{gather*}

---

- 主翼CDF
\begin{gather*}
C_{DF}=C_{F}*FF*\frac{S_{wet}}{S_{ref}}\\
C_{DF}= 0.003302*1.2425\frac{679.952263ft^2}{334.174856 ft^2}
\\
= 0.008348
\end{gather*}

- 機身CDF
\begin{gather*}
C_{DF}=C_{F}*FF*\frac{S_{wet}}{S_{ref}}\\
C_{DF}= 0.003302*1.2027\frac{758.0277353ft^2}{334.174856 ft^2}
\\
= 0.009008
\end{gather*}

- 垂直尾翼CDF
\begin{gather*}
C_{DF}=C_{F}*FF*\frac{S_{wet}}{S_{ref}}\\
C_{DF}= 0.003302*1.2425\frac{122.9307493ft^2}{334.174856 ft^2}
\\
= 0.001409
\end{gather*}

- 水平尾翼CDF
\begin{gather*}
C_{DF}=C_{F}*FF*\frac{S_{wet}}{S_{ref}}\\
C_{DF}= 0.003302*1.2425\frac{138.2970164ft^2}{334.174856 ft^2}
\\
= 0.001598
\end{gather*}

---

### 次要CDF

- 襟翼阻力係數
* $\frac{𝑏_{𝑓𝑙𝑎𝑝}}{𝑏}= 0.11$ 襟翼佔機翼總整體面積(從高升力攻角裝置部分得知)
* $𝛿_{flap} = 50degree = 0.8727 radians$
\begin{gather*}
𝐶_{𝐷,𝑓𝑙𝑎𝑝} ≈ 0.0023\frac{𝑏_{𝑓𝑙𝑎𝑝}}{𝑏}𝛿_{flap}\\
𝐶_{𝐷,𝑓𝑙𝑎𝑝} ≈ 0.0023*0.11*0.8727 \\≈ 0.0002207931
\end{gather*}
- 機身尾端修正阻力係數(這東西在小飛機值會超大我先忽略)
* $A_{max}$機身截面積
* 使用橢圓公式求得機身截面積 $A_{max}=3.801327111m^2=40.9171ft^2$
* 機身尾端傾斜角度$u=15 degree = 0.2618radians$
\begin{gather*}
C_{D,upsweep} = \frac{A_{max}}{S_{ref}}*3.83u^{2.5} = \frac{40.9171}{334.174856}*3.83*(0.2618)^{2.5}
\\
= 0.01645
\end{gather*}
- 起落架支架阻力係數
不知道起落架是要外露還是要收進飛機當中(問就是飛控)
\begin{gather*}
C_{DLG} = 4.05*10^{-3}\frac{W_{to}^{0.785}}{S}
\end{gather*}

---

| Information of CDF | Data |
|:------------------:|:-----------:|
| 主翼 | $0.008348$ |
| 機身 | $0.0090081$ |
| 水平尾翼 | $0.001598$ |
| 垂直尾翼 | $0.001409$ |
| 襟翼 | $0.0002208$ |
| 機身尾端修正 | $0.01645$ |
| TOTAL($C_{D,0}$) | $0.03703$ |

\begin{gather*}
C_{D}=C_{D0}+KC_{L}^2
\end{gather*}
* 橫向實黑線為最大升力係數
* 縱軸為CD0


roh =0.6531; % cruise_density at 20000ft (0.001267slug/ft^3)(0.6531kg/m^3)
S_w = 31.04586; % WET wing area (292.4500234ft^2) (31.04586m^2)
W=5608.42; % maximum takeoff weight (12364.46967lb) (5608.42kg)
CD0 =0.03702991401;
K = 0.04207109254;
V = linspace(0,400,10000);

CL=W./(0.5.*roh.*S_w.*V.^2);
CD=CD0+ K.*CL.^2;
plot(CD,CL,'blue');
hold on
plot(CD,-CL,'blue');
axis([0 0.5 -3 3]);
xline(CD0);
yline(2.680315704);
xlabel('CD');
ylabel('CL')

## 水平性能分析
:::danger
\begin{gather*}
性能分析的面積都用機翼扣除機身處的投影面積
\\
334.174856-41.72483266(chord*fuselage width)=292.450023ft^2
\end{gather*}
:::

假設飛機在無加速、水平的情形下飛行,則其推力與阻力大致相等;升力與重力相等

\begin{gather*}
T = D =qS(C_{D0}+KC_{L}^2)
\\\\
L = W = qSC_{L}
\end{gather*}

$\rho$ 為巡航高度空氣密度:

\begin{gather*}
\rho = 0.001267slug/ft^3 = 0.6531kg/m^3
\end{gather*}

將推力及升力兩式合併又可推得:

\begin{gather*}
\frac{T}{W} = \frac{C_{D0}+KC_{L}^2}{C_{L}}
\\\\
= \frac{1}{L/D}
\\\\
= \frac{qC_{D0}}{W/S}+(\frac{W}{S})\frac{K}{q}
\end{gather*}

將推力需求公式對速度微分,尋找最小阻力速度:

\begin{gather*}
V_{min,D} = \sqrt{\frac{2W}{\rho S}\sqrt{\frac{K}{C_{D0}}}}
\\\\
= \sqrt{\frac{2*12364.46967lb}{0.001267slug/ft^3 *334.174856ft^2}\sqrt{\frac{0.04207}{0.03703}}}
\\\\
= 266.7143478 ft/sec
\end{gather*}

我們保守估計最小阻力速度(Vmin,D),因此W是以最大起飛重量做計算:

\begin{gather*}
T_{R,min} = qC_{D0}S + (\frac{W^2}{S})\frac{K}{q}
\\\\
= 0.5*0.001267slug/ft^3 *(246.063 ft/s)^2*0.03703*292.450023ft^2+(\frac{(12364.46967lb)^2}{292.450023ft^2})\frac{0.04207}{0.5*0.001267slug/ft^3 *(246.063 ft/s)^2}
\\\\
= 988.7598704lb = 448.4939 kgw
\end{gather*}

**利用推力需求公式,將推力需求與速度之關係圖繪出:**


roh =0.001267; % cruise_density at 20000ft (0.001267slug/ft^3)(0.6531kg/m^3)
S_w = 292.450023; % WET wing area (292.4500234ft^2) (31.04586m^2)
V = linspace(0,400);
W=12364.46967; % maximum takeoff weight (12364.46967lb) (5608.42kg)
CD0 =0.03702991401;
K = 0.04207109254;
V_min = 266.7143478;

q = 0.5*roh.*V.^2;
CL=W./(0.5.*roh.*S_w.*V.^2);
D_ind=q.*S_w.*K.*CL.^2;
D_p=q.*S_w.*CD0;
D=D_p+D_ind;

plot(V,D_ind);
hold on
plot(V,D_p);
hold on
plot(V,D)
hold on
axis([0 400 0 2000]);
xline(V_min);
legend('induced drag', 'parasite drag','total drag');
xlabel('velocity(ft/s)');
ylabel('Lift(lb)');

## 航程分析

### 最大航程

For turbo prop

\begin{gather*}
R = 2\sqrt{\frac{2}{\rho S}} \frac{1}{tsfc}\frac{C_{L}^{1/2}}{C_{D}}(W_{0}^{1/2}-W_{1}^{1/2})
\end{gather*}

我們選用的引擎 PT6A-60A 巡航時之 tsfc 為:

$tsfc = 0.492$

飛機之航程最大值發生在$C_{L}^{1/2}/C_{D}$最大時,故由公式:

* $C_{D0} = 0.03703$
* $e = 0.7566$
* $AR =10$
\begin{gather*}
\\
\frac{C_{L}^{1/2}}{C_{D}}_{max} = \frac{(\frac{1}{3}C_{D0}\pi e AR)^{1/4}}{\frac{4}{3}C_{D0}}
\\
\\
= \frac{(\frac{1}{3}*0.03703*\pi *0.7566* 10)^{1/4}}{\frac{4}{3}*0.03703}
= 14.9063
\end{gather*}

- W0最大起飛重量
- W1為最大起飛重量減去燃料重量

\begin{gather*}
W_{1} = W_{0}-W_{f}
= 12364.46967 - 1063.50995 = 11300.95972lb
\end{gather*}

\begin{gather*}
R = 2\sqrt{\frac{2}{\rho S}} \frac{1}{tsfc}\frac{C_{L}^{1/2}}{C_{D}}(W_{0}^{1/2}-W_{1}^{1/2})
\\
\\
= 2\sqrt{\frac{2}{0.001267slug/ft^3* 292.450023ft^2}} \frac{1}{0.492}14.9063(12364.46967^{1/2}-11300.95972^{1/2})
\\
\\
= 688.3595005km
\end{gather*}

**最大航程 $688.3595005km，大於訂定的500km，符合設計要求**

### 最大續航力

\begin{gather*}
E = \frac{1}{tsfc}\frac{C_{L}}{C_{D}}ln\frac{W_{0}}{W_{1}}
\end{gather*}

飛機之續航力最大值發生在,當飛機以最小阻力速度飛行時。最小阻力速度又發生在升阻比最大時。故由最大升阻比公式:

\begin{gather*}
(\frac{C_{L}}{C_{D}})_{max} = \frac{\sqrt{\pi e AR C_{D0}}}{2C_{D0}}
\\
\\
= \frac{\sqrt{\pi *0.7566*10*0.03703}}{2*0.03703}
\\
\\
= 12.6678
\end{gather*}

\begin{gather*}
E = \frac{1}{tsfc}\frac{C_{L}}{C_{D}}ln\frac{W_{0}}{W_{1}}
\\
\\
= \frac{1}{0.492}*12.6678*ln\frac{12364.46967}{11300.95972}
= 2.3157hr
\end{gather*}

**最大續航力 $2.3157hr$**

## 起飛降落分析

### 起飛分析
失速速度定義為載具在最大攻角時,所能維持的水平飛行速度。由圖 7.1 及查表可
之最大攻角為$\alpha_{stall} = 11度$

\begin{gather*}
W = L =V_{stall}^2*C_{L,w} = 12364.46967lb
\\
C_{L,w} = 0.1186*(\alpha - (-7.75))
\\
\\
V_{stall} = 74.5512 ft/s
\end{gather*}

算出來的失速速度 74.5512 ft/s與當初訂定的失速速度 120 ft/s 計算時以74.5512 ft/s來估計理論最長範圍，但在實際飛行時以120ft/s

根據經驗公式
\begin{gather*}
V_{TO} = 1.15V_{stall}
\\
= 1.15*74.5512 = 85.7338ft/s
\end{gather*}

#### SG

* $T = 4693.92lb$
* $1050HP*2 = 2100HP = 1565969.7312W$
* $1565969.7312W / 75m/s = 20879.5964N$
* $20879.5964N = 4693.92lb(f)$
* alpha = 5 (根據上面經驗公式抓起飛角度)
* u = 0.1
* m = W/g
* g = 32.174ft/sec

\begin{gather*}
S_{G} = \int_{0}^{V_{TO}}\frac{vdv}{a} = \frac{1}{2}\int_{0}^{V_{TO}}\frac{dv^2}{a}
\\\\
L = v^2*C_{L} = 0.1186*(\alpha - (-7.75))
\\
D=v^2*C_{D}
\\
\\
F_{total} = ma = T-D- u(mg-L)
\\
a = \frac{g}{W}(T-D-u(mg-L))
\\
\\
S_{G} = \int_{0}^{V_{TO}}\frac{v}{\frac{T}{m}-ug+\frac{v^2(uC_{L}-C_{D})}{m}}dv
\\
\\
= 400.878ft = 122.1876144m
\\
\end{gather*}

alpha = 5
CD = (500*((593*alpha)/5000 + 18383/20000)^2)/(3783*pi) + 333535813873995/9007199254740992
CL = (593*alpha)/5000 + 18383/20000
T = 4693.92
m = 384.3
Vto =85.7338
u = 0.1
g = 32.174
f = @(v)v./(T./m-u.*g+(v.^2.*(u.*CL-CD))./m)
integral(f,0,Vto)

#### SR

\begin{gather*}
S_{R} = 2*V_{TO} = 2*85.7338 = 171.4676 ft = 52.2634m
\end{gather*}

#### STR
n 為 1.15,代入解 R,其中 R 是爬升時,被視為爬升曲線的半徑值

\begin{gather*}
n = 1+\frac{V_{TO}^2}{Rg} = \frac{L}{W} = 1.15 (經驗)
\\
R = \frac{V_{TO}^2}{(n-1)g} = \frac{V_{TO}^2}{0.15g}
\\
S_{TR} = Rsin\gamma = R(\frac{T-D}{W})
= 457.562ft = 139.4648976m
\end{gather*}

#### SCL

\begin{gather*}
S_{CL} = \frac{50-h_{TR}}{tan\gamma_{climb}}
\\
\\
h_{TR} = R(1-cos\gamma_{climb}) = \frac{V_{TO}^2}{0.15g}(1-cos(sin^{-1}\frac{(T-D)}{W} )) > 50ft
\\
\\
如果h_{TR} > 50ft, S_{CL}計為0
\end{gather*}

#### Total take off distance

\begin{gather*}
S = S_{G}+S_{R}+S_{TR}+S_{CL} = 1029.907685ft = 313.9158624 m
\end{gather*}

### 降落分析

根據經驗公式

\begin{gather*}
V_{TD} = 1.2V_{stall}
= 1.2*74.55116743 = 89.46140091 ft/s
\\
V_{50} = 1.3V_{stall}
= 1.3*74.55116743 = 96.91651766 ft/s
\end{gather*}

#### SA
\begin{gather*}
S_{A} = \frac{W}{F}(\frac{V_{50}^2-V_{TD}^2}{2g})+50
\\
近似
S_{A} = \frac{L}{D}(\frac{V_{50}^2-V_{TD}^2}{2g})+50
\\
\\
= 295.0788806ft = 89.94004279m
\end{gather*}

#### SFR

\begin{gather*}
S_{FR} = 3V_{TD}
\\
\\
=3*89.46140091
\\
\\
= 268.3842027ft = 81.803505m
\end{gather*}

#### SB

\begin{gather*}
S_{B} = 1.269S_{S_{A}}
\\
= 354.0946567 ft = 107.9280514m
\end{gather*}

#### Total landing distance

\begin{gather*}
S = S_{A}+S_{FR}+S_{B} = 917.55774 ft = 279.6715991m
\end{gather*}

#### 比較

| | $\alpha = 5, V_{to} = 85.7338ft/s$ | $\alpha = 5, V_{to} = 120ft/s$ |
|:--------------:|:----------------------------------:|:------------------------------:|
| SG | 122.1876144m | 235.2226639m |
| SR | 52.26335041m | 73.152m |
| STR | 139.4648976m | 204.1425127m |
| STL | 0m | 0m |
| Take off Total | **313.9158624m** | **512.5171766m** |
| SA | 89.94004279m | 161.5852951m |
| SFR | 81.803505m | 114.4987826m |
| SB | 107.9280514m | 193.9023541m |
| Landing Total | **279.6715991m** | **469.9864318m** |