CIV401: Numerical Methods Project - Design of an Airport Runway - Report Writing - Engineering Assignment Help

Assignment Task:

Task:

1. Introduction
Several airports in busy cities have taxiway and runway crossing vehicles highway (Fig. 1). You are the engineer who is responsible about the design of such an airport runway. Part of the runway is crossing the highway of the city over a bridge (Fig. 1). You need to design the airport runway by finding the minimum runway length and maximum deflection in the bridge slab.

2. Runway Design
The airport runway length (Fig. 2), called the takeoff distance, is divided into two parts. The first part called the ground roll (distance) xg defined as distance on ground before the airplane main landing gear (wheels) is no longer in touch with the ground, and the second part called the airborne distance xa when the airplane is not in touch with the ground before it clears an obstacle of a specifies height (Fig. 3), typically 15 m above the ground. The sum of the two distances is the minimum takeoff length, usually increased by 15 % as a factor of safety.

At the start point on the runway when the airplane is motionless, t = 0 and u = 0. The pilot releases the brakes and pushes the throttle to the maximum takeoff power of the engines to accelerate the airplane down the runway. At the end of the of the ground roll distance xg, the airplane must gain velocity slightly higher than the stall velocity in order to leave the ground and fly. Stall velocity is slowest speed a plane can fly to maintain level flight. Failure to obtain this velocity at end ground roll distance xg requires from the pilot to stop the airplane at the end of the runway (Fig. 4).

Consider Fig. 5 which shows the airplane at 3 positions at the ground; end of the distance xg before it is flying and at the end of the runway above the shown obstacle. In order to estimate the runway length, we need to apply the momentum equation of the moving airplane when it is on the ground and when it is flying. Fig. 6 shows the forces on the airplane when it moves on the ground and when it is flying. The major forces on the airplane when it is moving on the ground are the engine thrust T (driving force), the drag force D, the lift force L, landing gear (wheels) friction resistance R due to its weight W and friction ?. On the air there is no friction resistance. Notice that L is normal to the drag not vertical when the airplane is flying. The velocity of the airplane on its pass is V and u and v are its horizontal and vertical components respectively.

3. Slab Design
When designing a slab of a bridge you have to check the slab deflection among other factors. The edges of the slab may be treated as fixed support or hinged support depending on the size of the beams surrounding the slab to the slab thickness. Obtaining stresses and deflection on slabs
of irregular shapes or with complex load combinations can be challenging using analytic methods. Numerical methods can be a good alternative for those estimates. The differential equation to find the deflection in a slab (Fig. 7) is

4. Problem statement
You are the engineer who is responsible about the design of an airport runway. Part of the runway is crossing the highway of the city over a bridge (see figure 1). You are required to design the airport runway. The design elements include:

1) Estimate of the airport minimum runway length using Range-Kutta fourth order approximation for the momentum equation.

2) Estimate of the maximum deflection in the bridge using the central differential approximation for the deflection equation of plates (slabs). Also, find the minimum thickness of the slab to the nearest even number (cm) which makes the maximum deflection ≤ 5 mm for the fixed edges condition. Note that deflection w can be either positive or negative.

3) In your report, you need to provide an excel sheet or spread sheet for your detailed calculations.

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