ae 452 aeronautical engineering design iiae452/lecture2_air_loads.pdf · •an aircraft will...
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AE 452 Aeronautical Engineering Design IIAir Loads
Prof. Dr. Serkan Özgen
Dept. Aerospace Engineering
February 2017
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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.
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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.
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Level turn
6
• Corresponding turn rate:
𝜓 =𝑔 𝑛2 − 1
𝑉∞• Corresponding turn radius:
𝑅 =𝑉∞2
𝑔 𝑛2 − 1
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V-n diagram
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• V-n diagram depicts allowable load factors as a function of airspeed.
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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
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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.
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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!
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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.
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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.
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Gust loads
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Gust loads
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Gust loads
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