During our flight training we have all learned how to do the weight and balance calculations and we have been told that this is something we must do before every flight. Of course, even then, many of us thought this exercise was only good for watching the instructor’s reaction when you filled in his weight (for the examiner your estimate better had to be on the low side).

For me this was the state of affairs for the first 100 hours of my PPL “career”. However, lately I am flying more and more with passengers and luggage, so I thought I’d better brush up on my W&B knowledge. As things go these days, my first thought was whether there is an App for that, and sure enough there are plenty. In one of my next posts I will review an excellent application from Angell Development LLC by the name of WnB Pro.

Let’s talk first about the theory of W & B. As usual the FAA has very good materials on their web site (Aircraft Weight and Balance Handbook, FAA-H-8083-1A). I recommend reading this document if you are really serious about this stuff.

W&B is concerned within maximum and minimum weights as well as with the distribution of the weight in the aircraft. For the Piper we only need to know two weight limits, the maximum take off weight and the empty weight of the aircraft. The maximum takeoff weight can be found in the Pilot Operating Handbook or in the certification document on the FAA web site. For the latter you will need the serial number of the aircraft, because the PA28-161 was manufactured with different approved MTOW over the years. For the club Piper the MTOW is 2440 lb in the normal category. The empty weight is different for every aircraft, depending on the equipment installed or removed. The club aircraft weights 1544 lb. empty.

(In case you wonder what normal and utility category means: an aircraft operating in the normal category must be able to sustain a load factor of 3.8 and an aircraft operated in the utility category must be able to sustain a load factor of 4.4. For some aircraft there is also an acrobatic category with a load factor of 6.)

You may come across other weight limits, such as ramp weight, minimum landing weight, minimum fuel for take off etc. For the Piper you should consider the 200 lb limit for the baggage area, but going beyond hat weight will likely take you out of the approved W&B envelope anyway.

So let’s look at the balance calculation then. Intuitively we all understand that it matters where you put weight into an aircraft. Depending on the weight distribution the aircraft may be in perfect balance or it maybe tail or nose heavy. If it is nose heavy I have to pull on the yoke to achieve the right pitch attitude and if it is tail heavy I will have to push the yoke forward. It is also easy to imagine that the aircraft could be so nose or tail heavy that I need so much deflection of the elevator just to achieve level flight that I do not have enough deflection left to conduct other flight maneuvers such as take off or landing or turns.

This is where then W&B calculation comes in. The aircraft manufacturer designed the aircraft so that there is sufficient control of pitch attitude within certain limits of weight distribution. The W&B calculation determines whether your weight distribution is within those limits.

For the calculation you need to know three terms: weight, arm and moment.

The weight is usually given in pounds. A ballpark conversion factor to metric kg is 2.2.

The arm is the distance of the weight in the aircraft (also called the station) and a fixed point (the datum) somewhere on the aircraft’s longitudinal axis. Usually the arm does not tell you the distance to the center of gravity of the empty aircraft. Instead the manufacturer will choose a datum well forward of the center of gravity, so that all distances are positive and calculation errors are minimized. For light aircraft such as the piper, there will be an arm for the empty aircraft, for the front seats, the back seats, the baggage area and the fuel. There may also be an arm for the oil, but this is usually ignored or included in the arm for the empty aircraft. According to the FAA the arms for the club’s PA28-161 are as follows:

- Front seats: 80.5
- Back seats: 118.1
- Baggage compartment: 142.8 (max. 200 lb.)
- Fuel: 95
- Oil: 27.5 (usually ignored)

The moment is derived by multiplying weight and arm. It will only be needed in interim steps, so don’t look for it in the graph that shows the W&B envelope for normal and utility categories.

Now let’s get to the actual calculation. There are three methods to achieve the same results: the traditional paper and graph method, the “spread sheet” method and the iPad or iPhone application method.

For the PPL training, the exams and flight test you need to use the paper method. The graphs needed for this method are printed in the POH. Unfortunately, the graphs in the POH are barely legible. For training purposes, you could use the attached W&B sheet I created based on the POH.

The paper form has three elements: a table to note the results of the intermediate calculations, a graph to convert weight into moment for each weight position and a graph picturing the approved envelope for arm and weight combinations.

The process is relatively simple and can be followed more or less mechanically (see here for an example calculation):

- Note the weights for each station in the table. Enter the values in Pounds if you have them or in kg if you don’t.
- Enter the fuel in Gallons or in Liters.
- Convert the fuel quantity into pounds by multiplying the value in gallons with 6 or the liter value with 1.584
- Convert the Kg values into pounds by multiplying the kg value with 2.2
- You should have a pound value for each station now (some may be zero).
- Use the conversion chart to find the moment for each pound value. The vertical axis is the weight value in pounds. Find the value and move to the right to find the point where the weight intersects with the line for the station for which you want to find the moment. Now go down from this point to the horizontal axis, which gives you the moment in Thousands. Write down the moment in the respective station row in the table.
- You should have a moment for each station now (some may be zero).
- Add up all weights in pounds and all moments and note he result in the Total row in the table. If the weight exceeds the maximum weight you can stop here. You are too heavy!
- Divide the total value for the moments by the total value for the weight. This is your arm for the combined weight. Note down this value. If it is smaller than 83 or bigger than 93 you can top here. The weight is in the wrong place.
- Now go to the chart with envelope and find the arm value in the horizontal axis and the total weight in the vertical axis.
- If the intersection of the two values is within the envelope, you are fine. You should take note whether our point is in the normal or the utility category. There is a difference in approved maneuvers depending in which category you fall.

The spread sheet method works very similar to the paper method, but you let a spread sheet do the conversion between arm and moment. As mentioned before the moment is simply the product of the weight and the arm for the station to which the weight is applied. Of course, if you really use a spread sheet application all the conversions between pounds and kg and liter and gallons etc can be automated as well.

For the iPad application method, watch out for my review of the WnB Pro App in one of my next blog posts.