New packaging developed by the company you work for is known (based on tests) to protect the type of contents it is designed for provided that the package hits the ground at a speed less than 25 feet per second. The total weight of the package is 20 pounds, it is rectangular with dimensions 12” x 12” x 8”.

Is this packaging suitable for protection when carried by a delivery person?

EGR101: Introduction to Engineering Design - Module on Engineering Computing

Packaging Design and Assessment

by W. J. Palm

1. Understand the purpose of the problem.

The packaging material we are assessing is designed to protect a package against accidental damage when being carried by a person. It is not designed to protect the package when it is dropped off the Empire State Building.

2. Collect the known information. Realize that some of it might be discovered later to be unnecessary.

We have knowledge of the weight of the package, its dimensions, and the maximum allowable impact speed:

Weight=20 lbs

Dimensions=12” x 12” x 8”

Maximum impact speed = 25 feet per second

3. Determine what information you must find.

We want to determine the maximum height that the package can be dropped from without damage. We will use this measure as a means to assess different packaging materials.

4. Simplify the problem only enough to allow the required information to be obtained. State any assumptions you make.

To make the problem solvable (or tractable) we’ll make the following assumptions.

· The package is dropped from rest with no vertical or horizontal velocity.

· The package does not tumble or flutter.

· The effect of air drag is negligible.

· The acceleration due to gravity is constant.

5. Draw a sketch and label any necessary variables.

6. Determine which of the fundamental principles are applicable.

Newton’s Laws of Motion are applicable. The basic kinematics of a falling object with no air drag or initial velocity are expressed as:

· Height versus time to impact:

· Impact speed versus time to impact:

· Conservation of mechanical energy:

where v_i and t_i are the impact velocity and time respectively.

7. Think about your proposed solution approach in general and consider other approaches before proceeding with the details.

We can solve these equations is a variety of ways but the most direct solution is to solve the third equation for h:

Interpret the mathematics. If the mathematics produces multiple answers, do not discard some of them without considering what they mean. The mathematics might be trying to tell you something, and you might miss an opportunity to discover more about the problem.

The height for a given impact speed is not related to the mass of the object so some of our information above is unnecessary to solve our problem. It is important, however, that we know the box is fairly heavy relative to its size, and will only be falling from a small height. Because of these factors, we know that air resistance can be reasonably neglected.

Only one height results from a specific velocity (no multiple solutions).

8. Label each step of the solution process.

1. Set value of highest tolerable velocity (v_i)

2. Set the value for g

3. Solve for h in the equation above. It will be the maximum allowable height of drop

4. Determine if a delivery person would ever drop the package from more than this height (if no, than packaging is suitable, if yes it is not suitable).

9. Solve the problem. Assuming you are using a program to solve the problem:

· State the problem concisely.

Determine h assuming g is known and constant and the maximum v_i for the packaging material is known.

· Specify the data to be used by the program. This is the “input”.

v_i=25 ft/s, g=32.2 ft/sec²

· Specify the information to be generated by the program. This is the “output”.

h in ft.

· Work through the solution steps by hand or with a calculator using a simple data set.

This step does not really apply to our simple problem. We are going to use MATLAB as a calculator to form our solution directly with our actual input data. No need here to mess around with a simple data set and hand calculations.

· Write and run the program.

>> g=32.2;

>> vi=25;

>> h=vi^2/(2*g)

h=9.7050

· Check the output of the program with your hand solution.

Does not apply because we did not perform a hand solution.

· Run the program with your actual input data (if different from the simple data set) and perform a reality check on the output.

Answer seems reasonable, based on everyday experience with falling objects.

Checking the dimensions and units and printing the results of intermediate steps in the calculation sequence can uncover mistakes.

Unit analysis… ((ft/sec)^2)/(ft/sec^2) -> ft

· If the program will be used as a general tool in the future, test it by running it for a range of reasonable input data values; perform a reality check on these results.

Not applicable here as only one input is needed.

However, if you want to get fancy try this…

>> g=32.2;

>> vi=[1:1:50];

>> h=vi.^2/(2*g);

>> plot(vi,h)

>> xlabel(‘impact velocity allowed (ft/sec)’);

>> ylabel(‘height we can drop from (ft)’);

>> grid

10. Present your solution using graphs and data tables to good effect where applicable. Do not state the answer with any greater precision than is justified by any of the following:

· The precision of the given information.

· The simplifying assumptions.

· The requirements of the problem.

The packaging should be sufficient to protect the package from a fall of less than 9.7 feet. Thus, the packaging is suitable for being carried by a delivery person.

No tables or graphs are applicable here. If we use a more accurate value for g (say g=32.17) and we know that the maximum velocity is known with 2 decimal places of precision, we would be justified in stating the resulting height (h=9.71 feet) with two decimals of precision.

This document was originally created by Dr. Malcolm Daniels of the Department of Electrical and Computer Engineering and was modified by Dr. Russell Hardie.