In this post, I'll explain the principles behind the ballast spreadsheet; and how to make it easily adaptable for different models.

#### Development history.

Before going further, I should acknowledge the work of Pierre Rondel. A couple of years ago, Pierre kindly sent me his ballast sheet for the Needle 115. I found it extremely useful, and it soon found a permanent place in my transmitter box.However, when I tried to adapt Pierre's sheet for my new Stribog, I found that the Excel formulae were all too easily invalidated. In this post, I describe a modified method which employs a simpler structure, and array formulae. The result is a spreadsheet which is simple and easy to adapt.

Needle 115 ballast and spacers |

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The problem

When it comes to ballasting, my Stribog F3F is a fairly typical example. It can carry up to 10 slugs in a ballast tube in the fuselage. The model comes with a carbon wing joiner as standard, however I ordered mine with an additional steel joiner, weighing in at 1.3kg (I reserve this for high wind use). To make things complicated, the joiner axis is forward of the CG.Stribog F3F |

My spreadsheet provided the answer. It allowed me to simulate various combinations of joiner and fuselage ballast, and to identify the good ones.

Screenshot of ballast spreadsheet for Stribog |

Hopefully you can now see the usefulness of these spreadsheets! Let's now see how to design one from scratch.

#### Designing a spreadsheet

For the purposes of creating a ballast spreadsheet, we'll treat the model as a collection of 'components'. Each component has a weight (Wt), a quantity (QTY) and a centre of gravity (CG) relative to some fixed reference (by convention we use the wing root leading edge). Each component will end up as a column on the spreadsheet. The first task is therefore to identify the components.

The primary component is the

*empty model*, that is: the plane ready to fly but without ballast.- CG = cg of empty model from root leading edge
- Wt = weight of empty model
- QTY=1 (there's only one empty model and it's mandatory!)

Next, consider

*fuselage ballast.*This normally consists of slugs and spacers arranged in a tube. Each ballast location has a unique cg and therefore counts as one component:- CG = cg of ballast location, from root leading edge.
- Wt = weight of one slug
- QTY = 1 (slug) or 0 (spacer)

Rather than entering the CG for each slug individually, it's more convenient to calculate it from the slug's position in the tube, the location of the tube, and the length of a slug (for an example, see Stribog spreadsheet, link at end).

*wing ballast*. This is carried in pockets aligned perpendicular to the fuselage axis. Each pair of left/right pockets is treated as a single component. The total number of slugs is represented in QTY. To summarise:

- CG = distance of pocket centre-line to root leading edge
- Wt = weight of a 'standard' slug
- QTY = number of slugs in the pocket. Fractions can be used to represent non-standard slugs.

The same idea can be used to represent other types of component such as special ballast pockets for fine tuning of CG, steel joiners etc.

The total weight is the sum of the weight of each component. If there N components:

The overall CG is the sum of the

First, here's the CG expressed using a standard Excel formula. Each component contributes a term:

There are some obvious issues with this approach. First the formula is tricky to construct (lots of terms, and lots of clicking!). Secondly if a component is added or deleted the CG formula will break. Finally, the length of the formula depends on the number of components, so if you have a model with both wing and fuselage ballast, the length of the equation can get out of hand.

Fortunately Excel offers a concise alternative, in the form of

The formula is short and expressive (the ranges refer to complete blocks of QTY, Wt and CG values). Also, the cell ranges adapt as columns are inserted or deleted - this makes it easy to amend a sheet for a different type of model, or to add, say, a corrective pocket in the nose or tail.

To make an array formula, terminate it with Ctrl+Shift+Enter (note the curly brackets {} which are added automatically). For more info on array formulae, see array formula examples and guidelines. From my brief experiments, array formulae are supported by Excel, Google Sheets (available free with your Google account), and OpenOffice.

#### Equations for weight and CG

Two key outputs of the spreadsheet are the total weight and overall CG.The total weight is the sum of the weight of each component. If there N components:

**Total weight = SUM(Wt**_{1}*QTY_{1}+ ... + Wt_{N}*QTY_{N})The overall CG is the sum of the

*moments*about the wing root leading edge, divided by the total weight:**CG = SUM(Wt**

_{1}*CG_{1}*QTY_{1}+ ... + Wt_{N}*CG_{N}*QTY_{N})/Total weight

#### Spreadsheet structure

The equations can be implemented quite easily using Excel. On my spreadsheets, the components occupy a block of adjacent columns.- The first row contains the Wt values of each component
- The second row contains CG values
- Subsequent rows contain various combinations of QTY, to simulate particular ballast configurations.

#### CG calculation using standard and array formulae

Let's see how the CG equation may be implemented, using two different techniques.First, here's the CG expressed using a standard Excel formula. Each component contributes a term:

Typical CG calculation using standard Excel syntax |

Fortunately Excel offers a concise alternative, in the form of

*array*or '

*CSE' formulae.*Here is the CG calculation expressed as an array formula:

CG calculation using array formula |

To make an array formula, terminate it with Ctrl+Shift+Enter (note the curly brackets {} which are added automatically). For more info on array formulae, see array formula examples and guidelines. From my brief experiments, array formulae are supported by Excel, Google Sheets (available free with your Google account), and OpenOffice.

#### Sample spreadsheets using array formulae

- Stribog Mk 1 (fuselage ballast)
- Needle 115 (wing ballast)

*Remember to alter the input data for your particular model.*

**Always check on a CG scale before flying!**
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