Have you ever looked at a life-sized horse sculpture and imagined what it would be like to make one? Artist Kevin Hockley shared with us the steps he took in making the horse model shown above for a display at the Western Development Museum, Saskatoon, Saskatchewan. And guess what—math played a huge role!

What was the first step in creating this life-sized model of a galloping horse? Research. The display was to depict a native horse race event at a fair in the 1930’s. Many hours were spent gathering references of horses in action.

**1. How many decades ago did the native horse race event depicted in the display actually take place?**

Once the look of the horse was decided on, a small scale sculpture was created to work out the pose. Kevin prepared a maquette (*a small scale model*) to aid in determining the position of the horse’s legs, head, ears and other body parts.

Kevin explains “I use a 1:12 scale, meaning one inch on the maquette translates to 12 inches on the full size sculpture.”

**2. If you made a model with the horse’s front legs measuring 4 inches (10 cm) long, how long will the full scale horse model’s front legs be?**

**3. If the maguette model measured 6 1/4 inches (16 cm) from the front of the chest to the rump, what would the comparable measurement be for the full-sized model?**

From the maquette, a full scale model was generated in Styrofoam over a metal support armature. (*In sculpture, an armature is a framework, usually wood and/or metal, around which the sculpture is built.*)

Modelling clay was applied over the Styrofoam and all the musculature sculpted in. To help Kevin accurately sculpt the muscles, a small stall was constructed in the studio where one of his horses stayed for the duration of the sculpting. This allowed him the best possible reference by having a live model right in front of the work.

Angles, such as for the shoulder or pasterns, are not done mathematically but simply by whether it looks good to Kevin or not. “When I don’t have a live model to take actual measurements from, or my live model is a different size from the sculpture, then **proportions** play a huge role,” Kevin said.

Once the clay model was complete, a fiberglass mould was made and from this a fiberglass cast was created.

Math Talk – proportion: the relation of one part to another or to the whole.

There are certain standard, relative lengths of the different parts of a horse’s body that are considered ideal. The ideal **ratio** of the length of a horse’s head to their total body length (from the tip of the nose to the end of the rump) is thought to be 1 : 4.

Math Talk – ratio: Ratio says how much of one thing there is compared to another thing. In this case we are comparing the length of a horse’s head to its total body length. A ratio can be written as 1 : 4 (read as 1 to 4) or as a fraction 1/4.

**4. If you were creating a horse model out of clay, or even drawing a horse, and the length of the head measured 2 3/4 inches (7 cm), how long should you make the total length of the horse from the tip of its nose to the end of its rump?**

Kevin uses the length of the horse’s head as a base unit of measurement and all other measurements are then calculated by the number of head lengths.

For example, the length of a horse’s shoulder is generally one head in length, the femur (*a horse’s thigh bone*) is 2/3 head, and the body (chest to rump) is 2-1/2 times the head length.

**5. Express the relationship between the length of a horse’s head to its body length as a ratio.**

Let’s assume the full-sized horse model’s head measured 25 inches (64 cm).

**6. How long would you make the horse model’s femur?**

**7. How long would you make the length of the horse’s body?**

Glass eyes were installed and the whole model given a realistic paint finish.

Once installed in the exhibit, ground work simulating a race track was installed, and a native rider mannequin was mounted on its back.

1. How many decades ago did the native horse race event depicted in the display actually take place?

Answer: A decade is a period of 10 years.

We can use skip counting to count back from 2014. You want to know the number of decades so, skip count by 10.

2014 – 2004 – 1994 – 1984 – 1974 – 1964 – 1954 – 1944 – 1934. Now, count the number of decades: Counting back from 2014: 2004 is one, 1994 is two, . . . 1934 is 8. The native horse race event depicted in the display took place eight decades ago.

2. If you made a model with the horse’s front legs measuring 4 inches (10 cm) long, how long will the full scale horse model’s front legs be?

Imperial Answer: 12 × 4 = 48. The full scale horse model’s front legs will be 48 inches.

Metric Answer: 12 × 10 = 120. The full scale horse model’s front legs will be 120 cm.

3. If the maguette model measured 6 1/4 inches (16 cm) from the front of the chest to the rump, what would the comparable measurement be for the full-sized model?

Imperial Answer: 6 1/4 × 12 = 75. The full-sized model would measure 75 inches from the front of the chest to the rump.

Metric Answer: 16 × 12 = 192. he full-sized model would measure 192 cm from the front of the chest to the rump.

4. If you were creating a horse model out of clay, or even drawing a horse, and the length of the head measured 2 3/4 inches (7 cm), how long should you make the total length of the horse from the tip of its nose to the end of its rump?

Imperial Answer: 4 × 2 3/4 = 11. The total length of the horse would be 11 inches.

Metric Answer: 4 × 7 = 28. The total length of the horse would be 28 cm.

5. Express the relationship between the length of a horse’s head to its body length as a ratio.

Answer: 1 : 2 1/2

6. How long would you make the horse model’s femur?

Imperial Answer: 25 × 2/3 = 16.66. The length of the femur should measure approximately 17 inches.

Metric Answer: 64 × 2/3 = 42.66. The length of the femur should measure approximately 43 cm.

7. How long would you make the length of the horse’s body?

Imperial Answer: 25 × 2 1/2 = 62 1/2. The length of the horse’s body should measure approximately 62 1/2 inches.

Metric Answer: 64 × 2 1/2 = 160. The length of the horse’s body should measure approximately 160 cm.

Common Core:

3.MD.A Solve problems involving measurement and estimation of intervals of time

4.OA.A.2 – Multiply a 2-digit number by a 2-digit number: word problems

5.NF.B.5a – Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

6.RP.A Understand ratio concepts and use ratio reasoning to solve problems.

7.G.A.1 – Scale drawings and scale factors

7.NS.A.2c – Multiply fractions and whole numbers

7.NS.A.3 – Multiply fractions and mixed numbers: word problems

Photos:

All photos are courtesy of Kevin Hockley.

I want to make a horse head to look over a wall. This really helped me a lot as I have never attempted something like this.Thank you very much.