Giving math a real-life application is one of my favorite parts of FLL programming. With just a little practice, I have helped eight-year-olds understand and follow the distance to rotation formula.

## How to Do the Rotation Formula: R = D / C

### Step 1: Find the circumference of the wheel

You’ll need the radius (a) or the diameter (b) to find the wheel circumference.

#### a) If you know the radius, use C = 2πr

How this formula works | |

C = circumference | Remember to measure using the metric system (cm). |

2 = doubles the radius to get the diameter | |

π = 3.14 | To remember that π = pi (pronounced “pie”), read the numbers 3.14 upside down. They look like the word “pie”. The 4 looks like a “P”, the 1 looks like an “I” and the 3 looks like an “E”: 3.14 = PI.E … It’s more impressive when you write it out and show the kids. |

r = radius | The radius is the distance from the center of the wheel to its edge. |

#### OR

#### b) If you know the diameter, use C = πd

How this formula works | |

C = circumference | Remember to measure using the metric system (cm). |

d = diameter | See tip below. The diameter is the distance across the wheel through the center |

π = 3.14 | To remember that π = pi (pronounced “pie”), read the numbers 3.14 upside down. They look like the word “pie”. The 4 looks like a “P”, the 1 looks like an “I” and the 3 looks like an “E”: 3.14 = PI.E … It’s more impressive when you write it out and show the kids. |

r = radius | The radius is the distance from the center of the wheel to its edge. |

**Tip #1: **Although it’s difficult to read, the wheel diameter in mm is the first number written on each LEGO wheel. Convert that number to cm (divide by 10) and you’ve got your diameter to the nearest tenth.

### STEP 2: Measure the straight distance you need to travel in **cm**.

### STEP 3: Finally, it’s time to calculate the number of wheel rotations using the distance to rotation formula, R = D / C

How this formula works |

R = number of rotations |

D = distance you need to travel, which you measured in the last step |

C = circumference |

**Tip #2: **Both the distance and the circumference need to be in the same unit in order to work. You can’t divide inches into cm and get the proper number of rotations needed.

**Tip #3:** You can enter the number of rotations into the “move” block and then convert to degrees by hitting “degrees” after you entered the number from the equation. That way, if you need to add or subtract just a little to the distance you wish to travel, you will have an easier number to shave something off of than the larger rotations unit.

**Tip #4:** Large wheels have the largest percentage of error when programming moving and turning. Smaller wheels are more precise, but move slower – so it’s a trade off.

## How to CalculateTurns

Use one of two different methods: The “Quick” Way or The “Math” Way. I have found that kids younger than 5th grade do not take well to The Math Way for turns, but it’s worth spending a little bit of time explaining.

### Option 1: The “Quick” Way (recommended for calculating right turns)

- Use the “View” on the brick (on NXT, it’s the third button to the right on the first screen of the LEGO brick. It looks like a TV screen with an arrow in it.).
- Click the “motor degrees” and then choose which motor you wish to view – A,B, or C. You can only view one motor at a time, but if you’re using it to measure going straight you can choose your left or right motor to view.
- Hold one wheel still while carefully and slowly pushing the “turning” wheel forward. The degrees the motor senses will show up on your screen and give you a really good idea of about how many degrees your root will need to move to make your robot turn right.
- Take three readings and find the average or guess a number in the range you saw the robot measure. Three tries at this often produce three different degrees, so be sure to do it multiple times. Either get the kids to guess an average or teach them how to find the average of the three numbers.

### Option 2: The “Math” Way

Circumference of the robot*** x ( angle of turn / 360 ) = distance needed to travel

- Calculate the circumference of the robot by measuring the distance in between the two wheels from the center of each wheel. I will often move them just a little bit in or out so it makes a nice even number. 10.5 or 11 cm is very common. This is the radius of the robot’s full circle, so your robot’s C = 3.14r2.
- Take this number and multiply by the degree you wish to turn – 90, 180, etc., so 90/360 =1/4, 180/360=1/2.
- Figure out the turn you wish the robot to move: A right turn is 90 degrees. An about face (getting the robot to turn completely backwards) is 180 degrees, a ¾ turn is 270 degrees and a complete circle is 360 degrees. So moving our robot at a right angle would be like turning it 90 degrees on the circle, or 1/4 of the circle, so our equations would be C (of robot) x 1/4 = distance to be traveled (cm).

#### Now that we know how far our robot must travel, we can plug back into the equation above (R=D/C) and get the rotation necessary to turn a right angle.

Cheatsheet of equations in order | |

Circumference | C = 2πr C = πd |

distance a wheel must travel to turn | C (of circle traced) x Turn = D C x DegreeTurn/360 = D (This distance will be put into the more common formula R = D / C.) |

converting distance to rotation | R = D / C |

(optional) perecentage of error | ( theoretical C measurement – actual C measurement ) / theoretical C measurement or the shorter form: (t-a/t) x 100 = % of error |

This is above the “pay grade” of most beginner FLL engineers, ** but** do not underestimate their ability to use applied mathematics. Not only will this speed up your robotics game programming, it will give your kids confidence to do more. That said, if a child is uncomfortable using it, I wouldn’t press the issue. Allow them to work with the view until they feel better about applying the math, and they will come to the ideas you present to them sooner or later. Once they get a “view” answer, do the math slowly

*for*them and see how the the two compare. The more your teammates see the math in action, the more they will feel comfortable using it themselves. Suggestion: Allow them to use calculators, don’t make it a chore. We had a team member go from absolutely hating math to “not disliking it so much”. 🙂

I truly believe the FIRST family of programs is the most integrated form of STEM we can share with our students and kids, but we have to present it to them, or it may go unnoticed.

## 2 Comments. Leave new

hey, what would the rotations be for a 90 degree pivot on a wheel of a 21.666 cm long diameter? thanks! 🙂

(Thanks to Mr. Nyman for adding this option for EV3s.)

Take a yellow motor rotations block and store Measure->Rotations in a variable.

Travel until sensing a color

Measure->Rotations again, and subtract the value you stored in a variable earlier.

-or-

Take the yellow motor rotations block and reset it

Travel until sensing a color

Measure->Rotations