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AER1011 Flight Physics 1Week 9 Tutorial 9 Question Sheet
Answers should be given correct to 2 decimal places.
You may assume ISA conditions unless otherwise stated.
1. An aircraft has a mass of 10,000kg, wing area of 56m2, wingspan 15.8, Cd,0=0.015 and
k=0.056. The aircraft is equipped with two turbofan engines, each providing 15kN of thrust
at sea-level (assume that thrust provided is independent of speed). The runway is paved
and it is assumed that μ=0.02. If the maximum lift coefficient is 1.0 on take-off, and the
wings are at a height of 1.2 metres, what is the lift-off speed for the aircraft?
𝟐𝑾
𝒗𝑳𝑶 = 𝟏. 𝟐𝒗𝒔𝒕𝒂𝒍𝒍 = 𝟏. 𝟐√𝝆 = 64.16m/s
∞ 𝑺𝑪𝑳,𝒎𝒂𝒙
2. For the aircraft in Question 1, what is the minimum length of the runway required?
(𝟏𝟔𝒉⁄𝒃)𝟐 (𝟏𝟔𝟏.𝟐⁄𝟏𝟓.𝟖)𝟐
𝝋= = = 𝟎. 𝟓𝟗𝟔𝟐
𝟏+(𝟏𝟔 ⁄𝒃) 𝟏+(𝟏𝟔𝟏.𝟐⁄𝟏𝟓.𝟖)𝟐
𝒉 𝟐
𝑳 = 𝟎. 𝟓𝝆𝒗𝟐 𝑺𝑪𝑳,𝒎𝒂𝒙 = 𝟎. 𝟓 ∗ 𝟏. 𝟐𝟐𝟓𝟔 ∗ (𝟎. 𝟕 ∗ 𝟔𝟒. 𝟏𝟔)𝟐 ∗ 𝟓𝟔 ∗ 𝟏. 𝟎 = 𝟔𝟗𝟐𝟏𝟗. 𝟗𝟗𝟕𝑵
𝑫 = 𝟎. 𝟓𝝆𝒗𝟐 𝑺(𝑪𝑫,𝟎 + 𝝋𝒌𝑪𝟐𝑳 )= 𝟎. 𝟓 ∗ 𝟏. 𝟐𝟐𝟓𝟔 ∗ (𝟎. 𝟕 ∗ 𝟔𝟒. 𝟏𝟔)𝟐 ∗ 𝟓𝟔)(𝟎. 𝟎𝟏𝟓 + 𝟎. 𝟓𝟗𝟔𝟐 ∗
𝟎. 𝟎𝟓𝟔 ∗ 𝟏 ∗ 𝟏)=3349.36N
𝟏.𝟒𝟒𝑾𝟐
𝒔𝑳𝑶 = 𝒈𝝆𝑺𝑪 =
𝑳,𝒎𝒂𝒙 {𝑻−[𝑫+𝝁𝒓 (𝑾−𝑳)]}
𝟏.𝟒𝟒∗𝟗𝟖𝟏𝟎𝟎∗𝟗𝟖𝟏𝟎𝟎
𝟗.𝟖𝟏∗𝟏.𝟐𝟐𝟓𝟔∗𝟓𝟔∗𝟏.𝟎{𝟑𝟎𝟎𝟎𝟎−[𝟑𝟑𝟒𝟗.𝟑𝟔+𝟎.𝟎𝟐(𝟗𝟖𝟏𝟎𝟎−𝟔𝟗𝟐𝟏𝟗.𝟗𝟗𝟕)]}
=789.41 metres
3. The flaps are deployed on take-off in order to increase the maximum lift coefficient to 2.6.
What is the percentage reduction in the required runway length?
𝟐𝑾
𝒗𝑳𝑶 = 𝟏. 𝟐𝒗𝒔𝒕𝒂𝒍𝒍 = 𝟏. 𝟐√𝝆 = 39.79/s
∞ 𝑺𝑪𝑳,𝒎𝒂𝒙
𝑳 = 𝟎. 𝟓𝝆𝒗𝟐 𝑺𝑪𝑳,𝒎𝒂𝒙 = 𝟎. 𝟓 ∗ 𝟏. 𝟐𝟐𝟓𝟔 ∗ (𝟎. 𝟕 ∗ 𝟑𝟗. 𝟕𝟗)𝟐 ∗ 𝟓𝟔 ∗ 𝟐. 𝟔 = 𝟔𝟗𝟐𝟏𝟖. 𝟖𝑵
𝑫 = 𝟎. 𝟓𝝆𝒗𝟐 𝑺(𝑪𝑫,𝟎 + 𝝋𝒌𝑪𝟐𝑳 )= 𝟎. 𝟓 ∗ 𝟏. 𝟐𝟐𝟓𝟔 ∗ (𝟎. 𝟕 ∗ 𝟑𝟗. 𝟕𝟗)𝟐 ∗ 𝟓𝟔)(𝟎. 𝟎𝟏𝟓 + 𝟎. 𝟓𝟗𝟔𝟐 ∗
𝟎. 𝟎𝟓𝟔 ∗ 𝟐. 𝟔 ∗ 𝟐. 𝟔)=6008.66N
𝟏.𝟒𝟒𝑾𝟐
𝒔𝑳𝑶 = 𝒈𝝆𝑺𝑪 =
𝑳,𝒎𝒂𝒙 {𝑻−[𝑫+𝝁𝒓 (𝑾−𝑳)]}
𝟏.𝟒𝟒∗𝟗𝟖𝟏𝟎𝟎∗𝟗𝟖𝟏𝟎𝟎
𝟗.𝟖𝟏∗𝟏.𝟐𝟐𝟓𝟔∗𝟓𝟔∗𝟐.𝟔{𝟑𝟎𝟎𝟎𝟎−[𝟔𝟎𝟎𝟖.𝟔𝟔+𝟎.𝟎𝟐(𝟗𝟖𝟏𝟎𝟎−𝟔𝟗𝟐𝟏𝟖.𝟖𝑵)]}
=338.1 metres
Runway length is reduced by 57.17%
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