Center of Mass Computation Aids

Round displayed computation results to decimal places. Note that computed results are indicated with the symbol

Enable Diagnostics Display: Check this to record processing diagnostics on separate page(s). To see the separate page, you may have to enable "popups". Use this only if you really, really want to see details in the computation steps, because it slows down the processing and produces myriads of pages of "information"!

Planning Weight Additions
Computing CM Location by Weighing the Car
Ballast Dimension Planning

Planning Weight Additions

Most Pinewood Derby car builders start by constructing the wood frame and attaching the wheels and axles. Then they add weight (ballast) to the car to accomplish two goals: (1) increase the car's weight up to 5.0 ounces, and (2) move the Center of Mass (balance point) to an advantageous part of the car, usually toward the rear wheels.

This part of the page is an aid for computing the amount and location of weight additions to accomplish these goals. To use the aid, fill in the values that you know and hit "tab" and the script will fill in what can be derived from them.

The usual use of the page is to figure out how much weight to add where in order to make an unweighted car have a desired weight distribution. But, you can work the other ways, too! For instance, the end product and a weight addition plan can be used to tell what the unweighted car should look like!

Note: This page uses javascript to perform the calculations. To use the page, javascript must be enabled. Most folks have already set their browser that way.


Wheelbase: Inches

Dimension Before +    Add =    Total Units
Weight Ounces
CM Loc X Inches ahead of rear axle
CM Loc Y Inches above rear axle
Wt on Rear Ounces
Wt Dist Fraction of Wt under rear wheels

"Before" describes the physics of the unweighted Pinewood Car and includes wheels and axles.
"Add" describes the physics of additional weight, e.g dense lead, added to the Pinewood Car.
"Total" describes the physics of the result of combining "Before" and "Add".
"CM Loc" tells the location of Center of Mass, as measured from the center of the rear axle toward the front of the car.
"Wt on Rear" describes the Weight that would be measured on a scale if only the rear wheels of the car were supported on the scale and the front wheels were supported off the scale but level with the rear wheels.
"Wt Dist" is the ratio or fraction, e.g. 0.8, of the weight carried by rear wheels.

The "Roll" buttons transfer entered and computed values and record them as though they were entered. Then the source and add fields are blanked. This allows activities such as "incremental build-up" and "incremental decomposition" computations.

Computing CM Location by Weighing the Car

Some Pinewood Car builders like to have the car's Center of Mass (CM) low in the car. Measuring vertical CM location by balancing is difficult. This is an alternative procedure.


Wheelbase: Inches
How far are the front wheels lifted: Inches
Total Weight: Ounces

The following measurements are made with the cars supported on their wheels. This will probably require some sort of "cradle" so that the car body does not touch the wheel supports, especially when lifting the front of the car.

Rear Wheel weight with car level: Ounces
Rear Wheel weight with front wheels lifted: Ounces

Center of Mass Location:
Inches forward from rear axles (CMx)
Inches above axle plane (CMy)

Ballast Dimension Planning

Well, now that you have decided how much weight you need to add and have some idea of the place that it must fit, you must work out the details. How big will it be? How thick can it be?

Of these variables, the only "required" variable is material. Others will be computed from whatever values are supplied, so you can work from weight toward size or from size back to weight. Note that some of the materials are probably inappropriate for weighting a PWD car!

Weight: Ounces
Volume: Cubic Inches
Width: Inches, side to side
Thickness: Inches, top to bottom
Diameter, if cylinder: Inches
Length: Inches, front to back

Latest revisions:
12/8/2006 New!
12/9/2006 - Improve recomputation!
12/10/2006 - Reject non-numeric data entry; reject entry of inconsistent data values.
12/11/2006 - Redirect error alerts to popup!
12/12/2006 - Add Javascript note. Add link to "home". Move "diagnostics" checkbox to bottom.
12/18/2006 - Add CMx, CMy computation by weighing car.
12/20/2006 - Add diagrams.
12/21/2006 - Correct math error in CMy computation.
Add display precision specification.
12/23/2006 - Correct Loss of precision due to rounding error in "Planning Weight Additions" section.
Change scheme for indicating which values are supplied by user.
All results recomputed after changing "Round displayed computation results" specification.
12/24/2006 - Allow negative lift in "Computing CM Location by Weighing the Car" section, i.e. weigh with "nose down".
12/25/2006 - Correct handling of 0 and add CMy computations in "Planning Weight Additions".
12/27/2006 - Add "Ballast Dimension Planning".
12/28/2006 - Revamp indicator for distinguishing results of computation from inputs. Change "Computing CM Location by Weighing the Car" to multiway (bidirectional) computation.
12/29/2006 - Recompute all functions when precision is changed.
12/30/2006 - Correct units description of "Diameter, if cylinder"
3/8/2008 - Correct initial Lead Density value used in Ballast planning.
3/9/2008 - Improve Density table values used in Ballast planning.
12/8/2008 - Add "Roll Total to Before" and "Roll Before to Total" functions to CM Calc, Fix loop problem when "Add CMLoc X" is zero.

Known problems:
Copyright 2006, 2008 © by Stan Pope. All rights reserved.