AE 452 Aeronautical Engineering Design IIAir Loads

Prof. Dr. Serkan Özgen

Dept. Aerospace Engineering

February 2017

Maneuver loads

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Level turn

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• The greatest air loads on an airplane usually come from thegeneration of lift during high-g maneuvers.

𝑛 = 𝐿 𝑊, load factor and 𝑛 =1

𝑐𝑜𝑠𝜙

• The largest load the airplane is expected to encounter is called the limit load and the corresponding load factor is called the limit load factor.

• Ultimate load factor or the design load factor is the limit loadmultiplied by a factor of safety to account for material andworkmanship quality, design errors, uncertainty, etc.

• Factor of safety = 1.5 nultimate=1.5*nlimit.

Typical limit load factors

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Level turn

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• Stall limit for the maximum load factor (instantaneous turn):

𝐿 = 𝑛𝑚𝑎𝑥𝑊,𝐿 = 1 2𝜌∞𝑉𝑠𝑡𝑎𝑙𝑙2 𝐶𝐿,𝑚𝑎𝑥𝑆

𝑛𝑚𝑎𝑥 = 1 2𝜌∞𝑉𝑠𝑡𝑎𝑙𝑙

2 𝐶𝐿,𝑚𝑎𝑥

𝑊 𝑆

• The speed at which the maximum lift is equal to the allowablestructural load factor is the corner speed and provides themaximum turn rate for a given altitude.

• Modern fighters have a corner speed around 300-350 knots.

Level turn

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• Corresponding turn rate:

𝜓 =𝑔 𝑛2 − 1

𝑉∞• Corresponding turn radius:

𝑅 =𝑉∞2

𝑔 𝑛2 − 1

V-n diagram

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• V-n diagram depicts allowable load factors as a function of airspeed.

V-n diagram

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• Corner velocity: the slowest speed at which the maximum loadfactor can be reached without stalling.

• Dive speed: represents the maximum dynamic pressure, q∞. The point representing maximum q∞ and nlimit is important forstructural design. Exceeding Vdive may result in phenomena likewing divergence, control surface reversal, etc.

𝑉𝑑𝑖𝑣𝑒 = 1.5 ∗ 𝑉𝑐𝑟𝑢𝑖𝑠𝑒 or 𝑉𝑑𝑖𝑣𝑒 = 1.2 ∗ 𝑉𝑚𝑎𝑥 for subsonic airplanes

𝑀𝑑𝑖𝑣𝑒 = 𝑀𝑚𝑎𝑥 + 0.2 for supersonic airplanes

Sustained turn

• An aircraft will probably not be able to maintain speed andaltitude while turning at the maximum instantaneous turn rate.

• Sustained turn rate is usually specified in terms of themaximum load factor at a given flight condition that the aircraftcan sustain, e.g. 4-5g at M=0.9 at 30000 ft.

𝑇 = 𝐷, 𝐿 = 𝑛𝑊 ⇒ 𝑛 =𝑇

𝑊

𝐿

𝐷

• Load factor in a sustained turn increases when T/W and L/D increases.

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Aerodynamic and structural limitson turn performance

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Aerodynamic and thrust limitson turn performance

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Pull-up maneuver

• At 𝑡 = 0 𝜃 = 0 :

𝐹𝑟 = 𝐿 −𝑊 = 𝑊 𝑛 − 1 = 𝑚𝑉∞2

𝑅=

𝑊

𝑔

𝑉∞2

𝑅

• Solving for turn radius:

𝑅 =𝑉∞2

𝑔(𝑛−1)

• Solving for turn rate:

𝜓 =𝑉∞

𝑅=

𝑔(𝑛−1)

𝑉∞

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Pull-down maneuver

• At 𝑡 = 0 𝜃 = 0 :

𝐹𝑟 = 𝐿 +𝑊 = 𝑊 𝑛 + 1 = 𝑚𝑉∞2

𝑅=

𝑊

𝑔

𝑉∞2

𝑅

• Solving for turn radius:

𝑅 =𝑉∞2

𝑔(𝑛+1)

• Solving for turn rate:

𝜓 =𝑉∞

𝑅=

𝑔(𝑛+1)

𝑉∞

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Gust loads

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• The loads experienced when the airplane encounters a stronggust (when flying close to a thunderstorm or during clear air

turbulence encounter) may exceed the maneuver loads.

Gust loads

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• When an airplane encounters a gust, the effect is to increasethe angle of attack:

Δ𝛼 = 𝑡𝑎𝑛−1𝑈

𝑉∞≈

𝑈

𝑉∞

∆𝐿 = 𝑞∞𝑆 𝐶𝐿𝛼∆𝛼 =1

2𝜌∞𝑉∞𝑆𝐶𝐿𝛼𝑈

∆𝑛 =∆𝐿

𝑊=

𝜌∞𝑉∞𝐶𝐿𝛼𝑈

2 𝑊 𝑆 load factor due to a gust

increases for aircraft with low wing loading!

Gust loads

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• The assumption that an airplane instantly encounters a gustand this gust instantly effects the airplane is unrealistic.

• Gusts follow cosine-like intensity increase allowing aircraftmore time to react. This reduces the acceleration experiencedby the airplane.

Gust loads

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• Gust velocity:

𝑈 = 𝐾𝑈𝑑𝑒 , 𝐾: gust alleviation factor

𝐾 =0.88𝜇

5.3+𝜇, subsonic flight

𝐾 =𝜇1.03

6.95+𝜇1.03, supersonic flight

𝜇 =2 𝑊 𝑆

𝜌∞𝑔 𝑐𝐶𝐿𝛼, mass ratio

𝑈𝑑𝑒 = 30 𝑓𝑡/𝑠, standard vertical gust, produces n=3g loadfactor, suitable for CS23 airplanes.

Gust loads

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Gust loads

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Gust loads

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