Thursday, March 21, 2013

Estimating Exercise for Model Airplanes

I had come up with this lesson for estimating the cost to build a bunch of model airplanes, there never seemed to be much interest in it. Then I lost use of the server that it was hosted on, recently I ran across a pdf version. To me it seemed like a good practical exercise in mathematics.

The Exercise

Compute the Total Cost for balsa for 80 airplanes given the bill of materials for one airplane and the price list below. Break down your calculations for the two sources (mail order and hobby shop) and the two balsa types; sheet and stick. Allow for 10% waste on sheet wood and purchase one balsa stripper. Wing hold downs are made from the allowance for waste of the motor sticks (sheet wood only). For sticks allow two extra sticks for each type except 1/8" x 1/8" (wing hold down) only allow one stick extra.
To make the $20 minimum for mail order, add CA glue at $3.00 and CA Accelerator at $3.15, if order is still under $20, add second CA glue.
Calculate the number of packages of propellers needed for 80 planes, 35 propellers in a package. Make sure there are extra propellers but less than 35 extra. Add up all costs.Calculate how many feet of 3/32" rubber strip is in a one pound box. Make sure there is enough for 3 motors for each student (80 students), each motor 2 feet long.

Give your observations on the completed calculations, give advantages / disadvantages for the different options for purchase of balsa.
Bill of Materials Required for One Airplane

2 – 1/16" x 1/8" x 36" balsa strip

1 – 3/8" x 1/8" x 12" balsa motor stick

1 – 1/8" x 1/8" x 4" balsa wing hold down

1 – 6" plastic propeller assembly

3 – 24" lengths of 3/32" FAI Super Sport rubber

Price Lists

Balsa Price List

Balsa in 3" Sheets

Pre-cut Sticks

Additional Items Needed When Using Mail Order

Balsa Stripper $7.00

Shipping $8.00
Minimum Order $ 20.00

Note: If you use only sticks, the balsa stripper is not needed. This will save time as well.
** Purchasing From Hobby Shop, Assume Sales Tax
For this exercise assume 6% sales tax, this will vary between states, some states have none.

Propeller Price

Each plane needs a plastic propeller assembly that must be ordered in packages of 35. $10.56 per 35 plus $6.50 shipping. Shipping Note: there is only one shipping charge, so ordering more propellers the shipping is a smaller portion of the total cost.

Rubber Price

Each plane uses a loop of rubber that is a 24" loop of rubber strip including extra for the knot.

Each student needs three of these motors because of breakage. Compute how many motors would come out of one pound box of rubber. Use .0596 gram per inch as the weight for 3/32" rubber. There are 28.35 grams in one ounce.
Calculations will be for mail order only, as finding rubber strip in the correct size in a hobby shop is difficult and very expensive.
First calculate the length of rubber in feet in a one pound box knowing that rubber
weighs .0596 grams per inch for 3/32" width rubber that you will be using.

Price for one pound of 3/32" rubber is $23.00 + $5.00 shipping

Hints on How to Approach the Exercise


To compute the total cost for the different options, first compute the quantity of materials needed allowing for waste or broken pieces.

With the requirements, create tables of quantities needed of each material, cost per piece, calculations, and extra charges.
For the balsa in sheet wood, the width of the sheet (3") must be divided by the width of the strips needed; either 1/8" or 3/8". Remember to allow 10% waste.
Divide the number of pieces in each sheet into the total pieces needed to arrive at the number of sheets needed.
Three motor sticks can be cut from each 36" strip.

No doubt there are different methods to solve this, but I chose to convert grams to ounces and one pound to 16 ounces. Divide Ounces in a Pound by Ounce per Inch. Convert to feet.


Only need to make sure there are more propellers than needed when ordering propellers in packages of 35.

For an explanation of many aspects of simple aerodynamics with math problems check out my article Basic Aerodynamics With a Lesson

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