AOE 3024 FALL 2012 AERO PROJECT

TEAM 18

A new wing spar must be created given the data and parameters provided.

The design of the spar will be formulated by aspects of the engine placement, shape of the cross section and the material used.

The engine must be placed close enough to the plane to minimize the bending load but far enough to eliminate aerodynamic interference on the fuselage.

A well-chosen material for this wing spar will be low in cost, have a low density and have a high yield stress and Young’s modulus.

INTRODUCTION

Engine PlacementPART I

For our first design we went without the engine attached just to give us a base to start from.

Next we added to the code to determine the different effects from the placement of the engine, from 20ft to 90ft, would have on the beam in terms of meeting the given requirements for safety.

After doing this with an initial solid beam, we decided as a group that the best place to put the engine was as close to the fuselage as possible to keep the beam from bending too much and possibly even breaking.

ENGINE PLACEMENT

This was chosen mainly to be able to meet the requirements of Case 3’s static loading conditions because the further out you put the engine, the more the beam deflects at the tip (see Figures 1, 2, 3). Another reason we chose this location is because in the event of an engine failure it would produce a smaller moment about the center of the aircraft, which in turn would put less force on the rudder.

Given the simplicity of our beam we have concluded that 20ft would the best location for the engine on our design.

ENGINE PLACEMENT

Figure 1: Static displacement with engine at 20ft for solid beam (uy=-2.47664ft)

Figure 2: Static displacement with engine at 55ft for solid beam (uy=-2.68195ft)

Figure 3: Static displacement with engine at 90ft for solid beam (uy=-2.98233ft)

ENGINE DISPLACEMENT GRAPHS

Cross Section AnalysisPART II

During this design iteration we modified the initial box beam with the maximum breadth and width, and came up with different designs that changed the properties that we want the most, in particular the Moment of Inertia about the z-axis.

The reason we want Izz maximized is to resist bending due to the static load and the lifting force, which will reduce the stress and deflection on the z-axis.

CROSS SECTION ANALYSIS

The reason we decided to do a T beam initially is to test if small modifications will be enough to satisfy all cases for this problem

. The T beam will modify the cross section so that more area is away from the centroid, and thus better resist bending across the axis perpendicular.

The T beam failed in the static case, where it deflected more than the allowed 1.2 feet downward with all possible dimensions.

T-BEAM

T-BEAM

20 40 60 80Position on bar in ft

3

2

1

1

2

3uy ox in ft Displacement Resultant

Before we went into the next iteration, we decided to choose an arbitrary area that is reasonable and less than the maximum possible area for the beam.

This area will be the area that is used for all future comparisons to identify which design is best. The reason is that if the area is not normalized for each cross section the cross sections will not be evenly compared.

We chose the area to be 4.9 ft2. This number does not matter; the number could be any number as long as the dimensions do not exceed the given limits in the problem statement.

CROSS SECTIONAL ANALYSIS

The I-beam with the same area as the T beam, will give higher possible moments of inertia due to more area located away from the center.

We found the approximate max I zz without breaking the beam in stress by going through trial and error.

The I-beam was not successful in meeting all the critical conditions in lift and static loading with the given the following dimension and properties:

I-BEAM

I-BEAM

20 40 60 80Position on bar in ft

2.0

1.5

1.0

0.5

uyo x in ft Displacement Resultant

HOLLOWED SQUARE BEAM

The hollow square beam follows the same principles as the I-beam by putting mass away from the centroid but this time it is to resist bending about the y-axis.

The hollowed box beam did not meet the criteria for deflection in static loading with the following dimensions:

HOLLOWED SQUARE BEAM

We considered this beam because it can resist moments in the z and y axis well and resist stress.

This is because the beam is similar to the hollow beam and in addition to more local centroids that are away from the beam.

This final beam design also took consideration of carrying stress better than other cross sections since there are supports in the middle of the beam to help carry it.

DOUBLE I-BEAM

DOUBLE I-BEAM

With all of the designs analyzed we created a decision matrix to pick the most efficient cross section.

Here we ranked Izz as number one because we wanted to make sure the beam was able satisfy the conditions for static loading.

We ranked the ability to manufacture as number two in order to account for the price it will cost to manufacture the beam.

The third ranking was for performance on the I yy because it deals with the deflection due to the drag.

CROSS SECTION DECISION MATRIX

Choice of BeamAbility to Manufacture Izz Iyy Total

Total Rank

Double I Beam 4 1 1 12 1

T beam 1 4 3 15 4

I beam 2 2 4 18 2

Hollow Beam 3 3 2 15 2

CROSS SECTION DECISION MATRIX

Torsional Loads for Spar DesignPART III

Torsion would be created by the engine because it is placed below the wing spar. The torsion from the engine would make the wing spar want to rotate about the centroid of the chosen cross-section.

The weight of the fuel would also create a torsional force on the wing spar that would want to cause the spar to further rotate.

The aerodynamics of the airfoil also causes torsional forces to be applied on the wing spar.

Given more time on this spar design these torsional forces can be investigated and the overall design of the spar can be maximized to resist all force the spar encounters.

TORSIONAL LOADS

We are confident that the current wing spar design we are using now is worth investigating further because of the basic thought process on torsion.

When looking at wing spar designs, it is best to not have a cross section that has openings such as the cross section of I-Beams.

The closed cross section of the double I-Beam that we are currently proposing would be resistant to the torsional moment experienced inside the wing of an airplane.

Our wing spar did not come close to the yield stress of our material when undergoing bending stresses in the lifting, drag and static cases.

TORSIONAL LOADS

Choosing the Right MaterialPART IV

A decision matrix was created to choose among six different materials that were determined to be potential materials for the spar.

The six materials are 4140 Steel, AISI 1010 Steel, 6061 Aluminum Alloy, 7075 Aluminum Alloy, Nickel, Titanium, and Epoxy/Carbon Fiber Composite

The decision matrix is given below by Table 2 and the way it was utilized is as follows: Each category (density, elastic modulus, cost, etc.) is ranked on

importance from 1-5. Each material is scored from 1 through 7 (7 materials) with 7

being the worst ranking for the category and 1 being the best in that category.

The totals for each category are then summed and the material with the lowest score is the material of choice.

CHOOSING A MATERIAL

MATERIAL CANDIDATES

Table 1

Material Modulus Cost $/lb Yield Strength Density lb/ft^3

4140 Steel 29.7100E6 psi 0.450 94.98 ksi 490.752

Aluminum Alloy 6061 10.0000E6 psi 10.25 21.03 ksi 168.480

Aluminum Alloy 7075 10.4350E6 psi 19.06 72.94 ksi 176.250

Nickel 30.0000E6 psi 39.02 8.550 ksi 554.688

Titanium 16.8120E6 psi 57.77 20.30 ksi 281.664

Epoxy/Carbon Fiber 32.6090E6 psi 34.00 29.00 ksi 95.5230 

AISI 1010 STEEL 29.0075E6 psi 0.325 26.10 ksi 490.752

DECISION MATRIX

Table 2

Choice of the material Cost Yield Strength Density Modulus of

ElasticityCost to Manufacture Total

Importance of Each Category (1 most important) 1 5 2 4 3  

Aluminum Alloy 6061 3 5 2 7 3 80

Aluminum Alloy 7075 4 3 3 6 2 74

Titanium 7 6 4 5 5 94

4140 Steel 1 1 5 3 1 64

Nickel 6 7 6 2 4 90

Carbon Fiber 5 2 1 1 5 38

AISI 1010 Steel 2 4 5 4 1 76

From the results given by Table 1, it can be inferred that carbon fiber composite should in fact be the material selected.

However, that material was included in the decision matrix only as a comparison to see how it stacks up against steel.

The problem with carbon fiber is that it is very expensive and the manufacture of carbon fiber needs a lot of time and specific conditions in order to get a quality product

Since 4140 steel is a much easier material to work with, it led to 4140 Steel being chosen as the material to be used in the spar.

CHOOSING A MATERIAL

Developing the cost function for this spar is a simple calculation of the volume of the spar multiplied with the density of the material. When this value is multiplied with the cost of the material a final cost for the spar is obtained. The cost function is given as follows:

The area of the cross section for the beam is 4.9 ft2, length is 90 ft, the density and cost of 4140 Steel is 490.752 lb/ft3 and $0.45 respectively from Table 1.

CHOOSING A MATERIAL

The total cost of the spar as $41,738.73 is a very low cost compared to the other materials.

For comparison, a carbon fiber composite spar would cost $7,358,340.00.

The 4140 steel spar would weigh 97389 lbs while the carbon fiber composite spar would weigh 42125.6 lbs.

However, the difference in cost is what makes the 4140 spar win over the carbon fiber composite as the 4140 steel is $7,260,945.76 less.

The 4140 Steel passes all cases set for it, and therefore is deemed both a safe and cheap material to use in this wing spar.

CHOOSING A MATERIAL

The third and fourth best scoring materials according to Table 2 were 7075 Aluminum and AISI 1010 Steel respectively.

The aluminum is ruled out because it is far more expensive than the steel and would cost a total of $1,481,462.33 per spar whereas 1010 steel would have a price comparable to that of the 4140 Steel.

However, because the 1010 Steel did not score as well as 4140 Steel in the decision matrix it was ruled out as a possible material to be used and we made the decision to use 4140 Steel as our material for the spar.

CHOOSING A MATERIAL

V-N DIAGRAM

The V-N diagram was created using the given load and coefficient of lift maxes and the take-off weight of the aircraft. The stall velocity on the upper side of the flight envelope is 83.35 feet per second. The maximum velocity of the aircraft was taken if the airplane were to do a nose dive and fall under the aid of gravity only.

The wing spar we designed is safe, cost efficient and reliable.

The final design of the wing spar is the one with a “double-I” cross-section, 4140 Steel as the material, engine placement at 20 feet from the fuselage, total weight of 97389 lbs, and an estimated material cost of $100000 per wing spar.

According to the calculations and the decision matrix, the design achieved a good balance of safety, performance and cost. The wing spar meets all the requirements set forth, with a factor of safety of 1.15.

The deflection of the wing tip and the stress in the entire wing spar does not exceed the yield stress of the material in multiple situations, including taking off, one engine malfunctioning during cruise and static conditions.

CONCLUSION