Biomedical Engineering Modelling & Analysis Assignment -

Aim and Learning Outcomes:

To use appropriate software to solve a set of differential equations related to a topical engineering problem and use the solutions to make recommendations on the practicalities of the problem.

• Have a comprehensive knowledge and understanding of mathematical and computer models relevant to the mechanical and related engineering disciplines, and an appreciation of their limitations.
• Extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

Objectives

You will decide an appropriate software tool to generate a piece of code in order to solve the differential equations.

Use the software to determine the solution to the problem.

Comment on your results and assumptions of your analysis

Provide conclusions on your results in a report format.

Report Format

1. Introduction

2. Background and method used

3. Programme or code detail

4. Assumptions (bulleted list)

5. Analysis

a. Mainly images / tabulated data / commentary

6. Conclusions

The Problem:

It has been decided to use a small drone system to deliver medical supplies to a remote area in Africa. The drone can fly with a cruise speed (v_x) of 30 MPH and carry a mass of m (kg). The drone cruises at a height of h feet.

You are to estimate when to release the pay load in order for it to have a safe landing on the desired target point.

At release the drone will drop the package with a parachute which will fall to the ground with a velocity of v_y m/s.

This scenario can be modelled using the following set of differential equations:

mv^·_x = -½C_dxρA_xv_x²                                          (1)

mv^·_y = mg - ½C_dyρA_yv_y²                                    (2)

With m = mass, C_dy = vertical drag coefficient, C_dx = horizontal drag coefficient, ρ = density of air, A_x = cross sectional area facing horizontal air flow, A_y = cross sectional area facing vertical air flow, g = gravitational constant.

If you assume the wind pressure is negligible determine:

1. The velocity at which the package hits the group.

2. The time taken for the package to reach the ground.

3. The distance from the target the package needs to be released from by the drone.

For your analysis use the figures in the table below. You will be allocated a reference number by your tutor.

Take: A_x as 1.6m², A_y as 2.25 m², C_dx as 1.3 and C_dy as 1.75.