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## Scale Factors

A scale factor or a scale ratio is a way of showing the relationship of the actual size of a designed object and a scaled version of it. The scaled version can either be larger, the same size, or smaller. For example a scale factor of 2:1 means that the scaled object is double the size of the real one. A scale factor of 1:1 means the real object and the scale object are the same size. A scale factor of 1:2 means the scaled object is half the size of the real one.

## Scaling Cardboard for Prototype Models

Cardboard is a great material for making prototypes but it can give false impressions of a design if its thickness is not taken into account. Different planar materials have varying thicknesses. These thickness should be reflected in the prototype model.

Cardboard is often ~1/8" thick but if the design plans to use 3/4" (6/8) cardboard then a 1:6 scale model using 1/8" cardboard to represent 3/4" would mean that 12" would be only 2" in the model. This would be hard to work with since 2 feet would be represented by only 4".

A more sensible scale might be a 1:3 scale. At 1:3 scale you can double up 2 pieces of 1/8" plywood to represent 3/4" plywood. It also means that 12" is 4 inches in the scale model and 24" is 8" in the scale model. This is a more reasonable scale to work at.

Using an online scale converter we can type in 1:3 for the scale factor. Then you can type in the “real” length of your planned design from your ideation sketches and the scale converter will tell you what the scaled part should be.

## Inches vs Millimeters

If you grew up thinking in inches, it makes sense to design general dimensions in inches and to approximate sizes in inches since you have a learned intuition. However, it does not make sense to use inches to make a scale model. Use millimeters because you will make less math mistakes and it is much easier to count 100mm instead of 3 15/16" or 70 mm vs 2 3/4". Using the online scale converter you can have your input full scale sizes be in inches and the scaled dimensions be in mm for easy measuring on your ruler.

### 1:3 Scale Chart

The chart below is 1:3 scale. The dimensions on the left are in inches and are the “full scale” size. The measurements on the right show the smaller “scaled” dimensions. This shows the ease of mm vs inches. This chart is for illustrative purposes only. For more exact scaling or for using scale factors other than 1:3, use the online scale converter

Real Size Inches | 1:3 Scale Millimeters | 1:3 Scale Inches |
---|---|---|

5 | 42.3 | 1.6 |

8 | 67.7 | 2.6 |

11 | 93.1 | 3.6 |

22 | 186.2 | 7.3 |

32 | 270.9 | 10.6 |

44 | 372.5 | 14.6 |

48 | 406.4 | 16 |

Millimeters are small enough that their accuracy without the decimal is almost good enough. The same is not true of inches. .6 inches is not on the tape measure since the tape measure is divided by 1/8 and 1/16 of an inch. This method works for some measurements but or most dimensions it makes for messy conversions. For example 48 inches at 1:3 scale is exactly 16 inches but that does not work for 48.5 inches which is 16.1 inches at 1:3 scale.

The scale factor and unit of measure used is up to you, but for distances under 25 feet, just counting millimeters is a fairly easy and accurate way to go.

Make a cardboard model of your design. It is one thing to draw with pencil on paper, it is another to make a physical object. Problems and solutions that may not be apparent in your drawing will reveal themselves when you make a physical object. The model will be smaller than actual size.

You can cut the cardboard with hand tools or the laser cutter or both.

We will be using ¾” or ½” plywood for this project. You can use a ratio to scale your model.

Measure the cardboard and use a ratio calculator to scale your model dimensions.

First calculate the scale factor of your materials. If your single sheet of cardboard measures ~3.3mm and 3/4" plywood is ~18mm then you have a scale factor of 11:60. This website can easily calculate the scale factor for you. Online Scale Calculator

Once you know the scale factor then you can determine how big the pieces of your cardboard model should be based on that scale factor. This website lets you enter a scale factor and then enter in your final desired design dimension. For example if you want something 30" tall, you put in a scale factor of 11:60, type 30" in the “real length” and set the “scale length” to mm to get the scaled model size in mm. (You can use inches for your cardboard model but millimeters are soooo much easier to use, count, divide. Notice I put in 30" because for some distances. I know imperial units better but then I quickly convert to the easier to use metric system. Make sure you always double check your units.) This website will scale all your numbers. Online Scale Calculator