lab 6 vn diagram

8/12/2019 lab 6 vn diagram

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Parameters given; 0.970 0.985

0.89 1.000 0.995 0.05 0.012

,

0.016

max 2.0 1.1 1.1Calculate any constant or variable to use on the calculation

The air density at 25,000ft, , 0.0010663 The speed of sound at 25,000ft,

..

1.41716429.6 1015.91 /Master Equation

0.016+0.05( ) 0.012( ) + + 1 [ + 12 ]

25000 0.85(At 25000ft) 1000/ 16.667/

,=. 800(Turn Radius) 4000, 0.05


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Requirement 1:

Must be able to cruise at 25000ft with maximum velocity of M=0.85

Conditions for requirement 1:-

1, 0, 0, 0Master equation reduce to:-

0.016 0.012+0.05 List out given parameter and calculate;

0.00106630.0023769 0.4486

1015.91 /, 0.0010663 /; ; 0.851015.91 863.5235 / 12 12 0.0010663863.5235 397.5555 0.9700.985 0.9555

Hence, 0.95550.4486 397.55550.9555 0.016 0.012+0.05 0.9555397.5555 14.1794( )0.02556+2.559610 ( )


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Requirement 2:

Must be able to climb at a constant rate of 1000ft/min


0, 0, 1, Master equation reduce to:-

{ 0.016 0.012+0.05( ) + 1 }List out given parameter and calculate;

/ 16.6667 /

12 0.0023769120 17.11368 0.970 0.00237690.0023769 1

Hence,

0.9701 {17.1140.970 0.016 0.012+0.05(0.97011.8845 ) + 1125 16.6667} 0.274 +3.958510 ( )+0.134


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Requirement 3:

Must be able to perform a sustained turn of radius 800ft at 25000ft with velocity

M=0.85


0, 0, 0

Put the conditions into the master equation:-

{ 0.016 0.012 +0.05 ( )}

List out given parameter and calculate;

1015.91 /, 0.0010663 /; ; 0.851015.91 863.5235 /Turn radius, .. 800

1 863.5235 132.174800 28.99Since load factor 1, hence, 800800 800 863.5235280032.174 28.97 12 12 0.0010663863.5235 397.5555 0.00106630.0023769 0.4486


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0.9700.985 0.9555Hence,

0.95550.4486 {397.55550.9555 0.016 0.01228.97+0.0528.97 (0.9555397.5555 )} 14.1794+ 0.2148 ( )0.7405


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Requirement 4:

Must be able to takeoff with ground roll of 4000ft (assuming + at sealevel conditions.


1, 0, 0, Put the conditions into the master equation:-

{ 0.016 0.012+0.05( ) + 1 (12 )}


4000 1.2132.1740.00237692.0 Since

;4000 1.210.00237692.0

15.7150 Through integration and then differentiation of V2, the following value is obtained; 0.1273 0.00237690.0023769 1

1 20.0023769 12.0 20.5109 1.1 1.1 20.5109 22.5620


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2.872( )/

12 0.0023769 22.5620 0.6050

Hence ;

0.6050 0.016 0.012+0.05 0.6050

+

1

22.5620

1232.174 2.872 ( )3/2 1.9782 10 ( )+0.08032


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Requirement 5:

Must be able to achieve a horizontal acceleration 0.05ft/s2at 25000ft


0, 1, 0Put the conditions into the master equation:-

{ 0.016 0.012+0.05( ) + 1 (12 )}


1015.91 /, 0.0010663 ; ; 0.851015.91 863.5235 0.05Through integration and differentiation of V2, the following equation obatained;

0.1 0.00106630.0023769 0.4486

0.955500 0.9555 12 12 0.0010663863.5235 397.5555


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Hence ;

0.95550.4486 {397.55550.9555 0.016 0.012+0.05(0.9555397.5555 )

+ 1863.5235232.174 0.1863.5235}

14.1794+ 2.5596 10 ( )0.02401


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List of reduced master equation for each requirement;

Requirement 1

14.1794( )0.02556+2.559610 ( )

Requirement 2

0.274 +3.958510 ( )+0.134

Requirement 3

14.1794+ 0.2148 ( )0.7405

Requirement 4

1.9782 10 ( )+0.08032

Requirement 5

14.1794+ 2.5596 10 0.02401


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Figure 1 : Constraint Diagram

3

7.5


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As the rate of climb, turn radius, horizontal acceleration, and maximum cruise speed is

increased, the value of thrust loading (T/W) is going up. Since, any value of rate this

parameters greater than the specified parameter is satisfying the requirement, so the

region above the graph is acceptable.

As the value of take-off run increased, the value of thrust-to-weight ratio would drop.Since, any value of take-off run greater than the specified take-off run is not satisfying the

take-off run requirement, so the region below the graph is not acceptable.

Hence, the region above each graph is satisfying the performance requirements. In this

region, we are looking for the higher thrust to weight engine so that it has the lowest

operating cost. However, we want to maximize thrust-to-weight, hence the gradient of the

curve (turn) should be zero. Thus the design point chosen is (7.5, 3) . Therefore the wing

loading and thrust-to-weight are:

W/S = 7.5 lb/ft

2

T/W = 3

lab 6 vn diagram

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