Lesson 8: Aircraft Weight and Balance

Lesson 8: Aircraft Weight and Balance
Prof. H. Paul Shuch, Ph.D., CFII LSRM-A/GL/WSC/PPC, iRMT Heavy Chief Flight Instructor, Director of Maintenance AvSport of Lock Haven FAA Safety Team Lead Representative Piper Memorial Airport, Lock Haven PA Presentation Copyright © 2016

A FAASTeam WINGS Award Seminar
Presentation Copyright © 2016

Brought to you by: Wings of Williamsport Piper Memorial Airport
AvSport of Lock Haven Your FAA Safety Team Presentation Copyright © 2016

OBJECTIVES: Upon successful completion of this lesson, you will:
Define torque, datum, station, weight, arm, moment, and CG Given maximum gross weight and empty weight, compute useful load and payload Perform calculations of total weight and center of gravity Explain the importance of proper aircraft loading Understand why and how CG may vary throughout flight Ensure that the aircraft is always being operated within its safe loading envelope Presentation Copyright © 2016

DEFINITIONS On the slides that follow, we will define the following terms, which will be used throughout this lesson: Weight Datum Station Torque Arm Moment Center of Lift Center of Gravity Envelope Mean Aerodynamic Chord Presentation Copyright © 2016

Caution: Definitions are dry!

Definition Weight: The force exerted by a mass when it is acted on by the acceleration of gravity. Actually, we have several different weights to be concerned with. Maximum Gross Weight, set by the manufacturer (and limited by the aircraft’s certification rules) includes the aircraft, occupants, fuel, and baggage. For LSA airplanes, for example, it cannot exceed 1320 pounds. (Caution: it may be less!) Empty Weight typically includes the aircraft, installed equipment, engine oil, and unusable fuel. Useful Load is the difference between the two above figures, i.e., Maximum Gross Weight minus Empty Weight. Payload is what you can transport, assuming full tanks. So, it equals useful load minus the weight of maximum usable fuel. Presentation Copyright © 2016

Definition Datum: an arbitrary reference point, with respect to which locations and distances on the aircraft are measured. The datum can be defined as the firewall, instrument panel, leading edge of the wing, tip of the propeller spinner, baggage compartment bulkhead, or any other convenient, identifiable location that the manufacturer specifies. Note: Different aircraft may well use different references. For consistency, you must always measure every location on a given aircraft with respect to the same specified datum. Presentation Copyright © 2016

Definition Station: The physical location where a specific item (for example, a passenger or pilot in a seat, luggage in a baggage compartment, or fuel in a tank) is located in or installed on an aircraft Note: Stations are physically defined, and do not change with the loading of the aircraft (though what you place at a given station may). Presentation Copyright © 2016

Definition Torque: a measured rotational force applied at a specified distance. Note: All parts of the aircraft, and everything in it (people, fuel, equipment baggage, etc.), exert a torque on the aircraft in flight, when defined in relation to a specified datum. Although not generally expressed this way, all weight and balance calculations actually involve torques. If a force is expressed in pounds, and the distance at which it is applied is measured in inches, then the resulting torque is measured in inch-pounds. Presentation Copyright © 2016

Definition Arm: The location of a specific station, typically expressed in inches, measured with respect to the specified Datum. Note: measured arms can be to locations either ahead of, or behind, the specified datum. We specify arms as distances in inches forward of, or aft of, the datum respectively. The arm for a location forward of the datum is typically given a negative sign, while one aft of datum would be expressed as a positive number. Presentation Copyright © 2016

Definition Moment: Consider the forces exerted with respect to the datum by both the aircraft itself and its various contents. Moment is a torque being exerted, and is related to both the weight and the location of a given object. It is found by multiplying the weight of the item (empty airframe, quantity of fuel, pilot, passenger, or baggage item) by its arm (distance forward or aft of datum). If we measure arm in inches, and weight in pounds, then moment is expressed in inch-pounds (a familiar torque wrench unit). Note: moment can be positive or negative, depending upon the sign of the arm (positive for objects aft of datum, and negative for objects ahead of datum). Presentation Copyright © 2016

Definition Center of Lift: We know that the lift of an airfoil is what supports the aircraft in flight. It can be regarded as a force acting perpendicular to the surface of the wing. If we consider total lift to be a vector emanating from a particular point on the wing, its point of origin would be called Center of Lift (CL). Note: on a typical airfoil, CL is typically located near the thickest part of the wing. Presentation Copyright © 2016

Definition Center of Gravity: In unaccelerated level flight, the upward force of lift exactly counterbalances the downward force of gravity. Center of Gravity (CG) is the point of origin of the gravity vector. For lift and gravity to balance, one would expect CG to be somewhat close to the Center of Lift. Note: in the real world, planes (especially those with engines up front) tend to be nose-heavy. Thus, CG tends to fall ahead of CL. The exact location of CG varies with aircraft loading (and in this lesson you will learn how to calculate it precisely). Presentation Copyright © 2016

Definition Problem: But, if the CG is ahead of the CL, how can the plane ever possibly fly level? Solution: So far, we’ve been talking only about the Center of Lift of the wing (an airfoil). But, the horizontal tail is also an airfoil, with lift in the down direction. It is the downward lift of the tail that counteracts the downward force of gravity acting on the forward CG. This balances the aircraft for level flight. The amount of downward lift exerted by the tail is controlled with elevator (and elevator trim keeps it where you want it). Presentation Copyright © 2016

Definition Envelope: For every aircraft, there are limits to where the CG must fall for safety and stability. These limits vary with Gross Weight. A loading envelope is a diagram that shows the range of acceptable CG values, as the loaded Gross Weight changes. Note: an aircraft loaded out of the safety envelope is an accident waiting to happen! Thus, we calculate weight and CG before every flight, and plot them on an envelope diagram. Presentation Copyright © 2016

Definition Mean Aerodynamic Chord: Thus far, we have assumed CG would be described in inches fore (or aft) of datum. Since for safe operation the CG will always fall somewhere along the chord line of the wing, we could also describe CG as a point a certain percentage along the chord line (with 0% MAC indicating the leading edge of the wing, and 100% MAC referring to the trailing edge). Note: For a straight, symmetrical (“Hershey Bar”) wing, the chord is the same all the way from wing root to wing tip. If the wing is swept or tapered, the chord changes along its length. We would then have to compute the average (“mean”) chord, and express CG as a percentage of Mean (average) Aerodynamic Chord, or MAC. Presentation Copyright © 2016

Which of the following items is commonly measured in inch-pounds?
Datum Center of Gravity Center of Lift Moment Mean Aerodynamic Chord Presentation Copyright © 2016

HOW IS AN AIRCRAFT WEIGHED?

The plane must be reweighed any time equipment is added or removed.
After all standard equipment has been installed, all usable fuel is drained. The plane is placed on scales, and its total empty weight is measured directly. This is done by the manufacturer before the plane receives its airworthiness certificate, and is recorded on the aircraft’s official Weight and Balance form. The plane must be reweighed any time equipment is added or removed. Alternatively, weights of any equipment items or accessories added or removed can be used to recompute a new empty weight. The W/B form must then be updated. Presentation Copyright © 2016

Determining Total Weight
Before any flight, the weight of pilot, passengers, fuel, and baggage is added to the empty weight of the aircraft (obtained from the W/B records). The sum of these weights must be below the aircraft’s specified maximum gross weight. Exceeding maximum gross weight will result in increased takeoff roll and stall speed, reduced climb performance, and possible overstressing of the airframe. Presentation Copyright © 2016

Determining Total Weight (example)
Empty weight = pounds Pilot = pounds Passenger = pounds Baggage = pounds Fuel = 30 gal x 6#/gal = pounds Total takeoff weight = pounds Maximum Gross Wt = pounds Weight margin = # below max Presentation Copyright © 2016

Total Weight Shortcut (example 1)
If you happen to know your aircraft’s useful load (which you should): Maximum Gross Wt = pounds Empty weight = pounds Useful load = pounds All you need do before flight is add pilot, passengers, fuel, and baggage weights, and ensure they fall below that figure. [ = 535 < 570] Presentation Copyright © 2016

Total Weight Shortcut (example 2)
If you’re flying with full fuel, and you happen to know your aircraft’s payload (which you should): Useful load = pounds Fuel weight = 30 gal x 6#/gal = pounds Payload = pounds All you need do before flight is add pilot, passengers, and baggage weights, and ensure they fall below that figure. [ = 355 < 390] Presentation Copyright © 2016

Using a wt/bal Worksheet (1)
Here is a typical loading chart for a Light Sport Aircraft. For now, you can ignore the columns marked Arm and Moment. The Weight indicated next to “Plane” is its measured empty weight. Presentation Copyright © 2016

Using a wt/bal Worksheet (2)
Under the “Weight” column, write the weights of the occupants, fuel, and baggage. Remember that each gallon of AvGas weighs six pounds. Add up all the figures in the Weight column to get total weight. (We’ll come back to this worksheet later.) 170 150 180 35.5 1281 Presentation Copyright © 2016

Adjusting Total Weight
Should the aircraft’s specified maximum gross takeoff weight be exceeded, the pilot must remove baggage, passengers, or fuel, to bring total weight within limits. If fuel is reduced, the range of the aircraft must be recomputed, and leg lengths adjusted (or fuel stops added to the trip, as required). Taking off over-gross is not just contrary to FARs; it is also unsafe! Remember that stall speed increases with weight. Above 1320#, for example, an LSA may stall at above the maximum allowable 45 KCAS. Presentation Copyright © 2016

Payload of an aircraft includes all of the following except:
pilot passengers fuel baggage It includes them all Presentation Copyright © 2016

DETERMINING EMPTY WEIGHT CENTER OF GRAVITY

I suppose we could place the empty aircraft on a teeter-totter (the child’s playground toy consisting of a plank, pivot, and fulcrum), and slide the plane back and forth until it is exactly balanced (level). Where the fulcrum ended up with respect to the airframe would then be the EWCG. We could specify its location in inches fore or aft of datum. Presentation Copyright © 2016

But wait! Remember that the manufacturer already placed calibrated scales under each of the plane’s wheels, when reading total weight. If the plane was level during weighing, and if we know the exact location of the three wheels relative to the selected datum, it’s now possible to compute EWCG. (Fear not, the manufacturer of your aircraft has already done this for you! Check your wt/bal documents.) Presentation Copyright © 2016

Here’s an example of a full aircraft weighing experiment, including all the calculations. The CG has been computed both in inches aft of datum, and also as a percentage of mean aerodynamic chord (MAC). Your actual wt/bal documents may show one, or the other, or both. Presentation Copyright © 2016

DETERMINING OBJECT ARMS

For now, you can ignore the column marked Moment.
Here is the typical loading chart we introduced earlier. Note that all Arms are specified in inches aft of Datum. For now, you can ignore the column marked Moment. 170 150 180 35.5 1281 Presentation Copyright © 2016

Remember, the Station labeled “Plane” represents the empty aircraft.
The Weight shown next to “Plane” is still the measured aircraft empty weight. The Arm shown next to “Plane” is actually the computed or measured EWCG. All of the other Arm values come from the POH or AOI. 170 150 180 35.5 1281 Presentation Copyright © 2016

We’ll come back to this worksheet in a moment.
Before we can tackle the third column, we need to talk a bit about Moment and Torque. 170 150 180 35.5 1281 Presentation Copyright © 2016

Let’s build a Torque Wrench

Automating the process

The fundamental weight and balance equation is: Weight X Arm = Moment
Remember that Weight is a force, Arm is a distance, and Moment is a torque. So, this equation can be rewritten as: Force X Distance = Torque I call this the Torque Wrench Equation, and we will use it for computing aircraft weight and balance. Here’s why: Presentation Copyright © 2016

Recall that Moment is simply a measure of Torque, the result of a turning Force being applied at a specified Distance. Consider a 24 inch torque wrench, being used to tighten a bolt. If we pull with 10 pounds of force, at a distance of 24 inches from the fastener, we have applied a torque of [24 inches x 10 pounds = 240 inch pounds]. Moments are calculated similarly, by multiplying a force (in this case, weight) by a distance (in this case, arm). So, moment is measured in inch pounds. Presentation Copyright © 2016

You can now calculate the remaining moments, by multiplying across.
This is the same loading chart we worked with earlier. Here, the torque (moment) of the empty aircraft has already been computed for you. We multiplied its empty weight (745.5 pounds) by its EWCG of 10.16”, to get inch-pounds. You can now calculate the remaining moments, by multiplying across. 170 150 180 35.5 1281 Presentation Copyright © 2016

If you came up with something like this, you’re getting the hang of computing moments!
170 150 180 35.5 1281 3646.5 3217.5 4815 1514.1 Presentation Copyright © 2016

Bear with me, we’re getting there! We now have moments in inch lbs.
The total torque acting on the loaded CG is now found by simply adding up the individual moments (right column). 170 150 180 35.5 1281 3646.5 3217.5 4815 1514.1 Presentation Copyright © 2016

In our example, the Moments are all positive numbers
In our example, the Moments are all positive numbers. Depending upon the location of the Datum, some of the Moments might well have come out negative. So, be sure to pay attention to signs when you add them up! 170 150 180 35.5 1281 3646.5 3217.5 4815 1514.1 Presentation Copyright © 2016

CALCULATING CENTER OF GRAVITY

Remember the torque wrench equation?
Torque (‘’#) = distance (‘’) x force (#) If we use a little algebra, rearrange and we can solve for distance: Distance (inches) = torque (inch pounds) / force (pounds) Which is the same as saying: CG (inches) = moment (inch pounds) / weight (pounds) Presentation Copyright © 2016

Well, we already have total weight and total moment
Well, we already have total weight and total moment. So, to find CG, all we have to do is divide: 170 150 180 35.5 1281 3646.5 3217.5 4815 1514.1 16.2” Presentation Copyright © 2016

Remember, we got here from the Torque Wrench Equation:
CG (inches) = moment (inch pounds) / weight (pounds) We now know the Center of Gravity of the loaded airplane! But, is that a safe CG? To find out, we need to use a Loading Envelope. Before we do that, let’s practice… Presentation Copyright © 2016

Not enough information to answer
Assume an aircraft has a total loaded weight of 1000 pounds, and total moment is 20,000”#. Find the resulting CG. 20 pounds aft of datum 20 pounds ahead of datum 20 inches aft of datum 20 inches ahead of datum Not enough information to answer Presentation Copyright © 2016

ENSURING LONGITUDINAL STABILITY

Let’s take a look at a typical airplane in level flight:
Notice that the loaded CG is ahead of the wing’s Center of Lift. In other words, the plane is deliberately nose-heavy. Why is this important? Presentation Copyright © 2016

The wing and the tail are both airfoils.
The wing has lift in the up direction. The tail has lift in the down direction. Because the plane is nose-heavy, between the three forces, the plane exactly balances. Presentation Copyright © 2016

Let’s assume the plane speeds up for some reason.
More airflow across the wing increases lift; the plane climbs. But more airflow across the tail increases its down lift. The nose pitches up. Since pitch controls airspeed, this slows down the plane, decreasing airflow across the wing, thus decreasing lift and restoring level flight. Presentation Copyright © 2016

Now assume the plane slows down for some reason.
Less airflow across the wing decreases lift; the plane descends. But less airflow across the tail reduces its down lift. The nose pitches down. Since pitch controls airspeed, this speeds up the plane, increasing airflow across the wing, hence increasing lift and restoring level flight. Presentation Copyright © 2016

Thus, when properly trimmed, the plane maintains a constant airspeed.
We use the elevator to compensate for small airspeed deviations which detract from stable, unaccelerated flight (and then use trim to reduce the amount of stick or yoke pressure necessary to achieve this goal - think of trim as a kind of Cruise Control). Presentation Copyright © 2016

Several factors affect how an airplane will stall, especially weight and balance.
Forward CG: As the center of gravity moves forward, the down force required by the tail is increased (airplane needs higher angle of attack). With a forward CG, the airplane will stall at a faster speed, but it will be more difficult to stall and easier to recover. Forward CG also gives the tail more leverage, and increased control effectiveness. Presentation Copyright © 2016

However, a CG too far forward can interfere with the aircraft’s ability to flare or round out for landing. And, since a fore CG increases stall resistance, it may make a full-stall landing impossible (remember that the objective of a proper flare is to stall the aircraft just inches above the runway). Presentation Copyright © 2016

Several factors affect how an airplane will stall, especially weight and balance.
Aft CG: As the center of gravity moves back, the down lift required by the tail is decreased. Since the process of generating lift also causes induced drag, an aft CG thus decreases drag, improving cruise speed. But, the aircraft will stall more readily, and stall recovery becomes more difficult. Rear CG also gives the tail less leverage, and decreases control effectiveness. Presentation Copyright © 2016

Stall Recovery: Let’s assume the wing exceeds its critical angle of attack in flight, inducing a stall. Because the CG is ahead of the center of lift, the plane pitches down. Since pitch controls airspeed, the plane accelerates, providing more airflow across the wing, restoring lift and thus breaking the stall. Presentation Copyright © 2016

Of course, improper pilot actions can hamper stall recovery.
Holding back-pressure on the stick or yoke increases the downward lift of the elevator, possibly keeping the angle of attack above critical. This is why we relax elevator back-pressure when recovering from a stall. Presentation Copyright © 2016

It is very important that the airplane be properly loaded, with the CG within the acceptable limits.
To calculate where the CG is, use the information in the Pilot’s Operating Handbook (POH) or the Airplane Operating Instructions (AOI). The empty weight and loading data must come from the documents specific to that airplane. Presentation Copyright © 2016

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