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**Post-Solo Training Module**

Flight Briefing: Lesson 12 Weight and Balance In cooperation with AvSport of Lock Haven , Piper Memorial Airport, Lock Haven PA (by H. Paul Shuch, Chief Flight Instructor)

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**Lesson 12 Objectives Upon completion of this module, you will:**

Define datum, station, arm, moment, and CG Perform calculations of total weight and center of gravity for a Light Sport aircraft Explain the importance of proper aircraft loading Understand why CG varies throughout flight Ensure that the aircraft is always being operated within its proper loading envelope

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Definition of Terms On the pages that follow, we will define the following terms, which will be used throughout this lesson: Datum Weight Arm Moment Center of Lift Center of Gravity Envelope Mean Aerodynamic Chord

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Definition of Terms 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.

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Definition of Terms Weight: actually, we have several different ones to be concerned with. Maximum Gross Weight, set by the manufacturer (and limited by the Light Sport Aircraft rules) includes the aircraft, occupants, fuel, and baggage. For LSA airplanes, 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.

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Definition of Terms Arm: The location of a specific point on the aircraft (for example, the center of the seat, baggage compartment, or a fuel tank), expressed with respect to the 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.

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Definition of Terms 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).

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Definition of Terms 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.

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Definition of Terms 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, CL tends to fall ahead of CG. The exact location of CG varies with aircraft loading (and in this lesson you will learn how to calculate it precisely).

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Definition of Terms 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.

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Definition of Terms 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.

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**Determining Empty Weight**

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.

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**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.

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**Determining Total Weight (Example)**

Empty weight = pounds Pilot = pounds Passenger = pounds Baggage = pounds Fuel = 30 gal x 6#/gal = +180 pounds Total takeoff weight = pounds Maximum Gross Wt = pounds Weight margin = # below max

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**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, passenger, fuel, and baggage weights, and ensure they fall below that figure. [ = 535 < 570]

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**Total Weight Shortcut (example #2)**

If you happen to know your aircraft’s payload (which you also should): Useful load = pounds Full fuel = 30 gal x 6#/gal = pounds Payload = pounds And, if you plan to take off with full fuel, All you need do before is add pilot, passenger, and baggage weights, and ensure they fall below that figure. [ = 355 < 390]

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**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.

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**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

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**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#, an LSA will stall at above 45 kts.

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**Determining Empty Weight CG (1)**

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.

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**Determining Empty Weight CG (2)**

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.)

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**Determining Empty Weight CG (3)**

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.

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**Determining Object Arms**

The location of each area in the airplane to which weight can be added is called a Station. Locations of Stations are typically measured in inches forward or aft of the specified Datum. You will need to determine the Station for each of the seats, fuel tanks, and baggage compartments in your aircraft. Your Aircraft Operating Instructions (or Pilot’s Operating Handbook) should list stations for the pilot, passenger, baggage, and fuel. The distance from the Datum to any specified Station is called its Arm.

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**Determining Object Arms (2)**

Here is a 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

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**Determining Object Arms (3)**

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

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**Computing Individual Moments (1)**

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. 170 150 180 35.5 1281

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**Computing Individual Moments (2)**

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 a multiplying force (in this case, weight) by a distance (in this case, arm). So, moment is measured in inch pounds.

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**Computing Individual Moments (3)**

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” You can now calculate the remaining moments, by multiplying across. 170 150 180 35.5 1281

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**Computing Individual Moments (4)**

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

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**Computing Total Moment**

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

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Computing Loaded CG (1) Remember the torque wrench equation? Torque (inch pounds) = distance (inches) x force (pounds) 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)

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Computing Loaded CG (2) 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”

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**CG (inches) = moment (inch pounds) / weight (pounds)**

Computing Loaded CG (3) 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.

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Computing Loaded CG (4) There are computer spreadsheets available to help expedite the computation of weight and balance, but officially, this is how you determine the location of the CG.

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**Loading for 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?

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**Loading for Longitudinal Stability (2)**

Notice that 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 two, the plane exactly balances.

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**Loading for Longitudinal Stability (3)**

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, restoring it to level flight.

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**Loading for Longitudinal Stability (4)**

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, restoring it to level flight.

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**Loading for Longitudinal Stability (5)**

Thus, when properly trimmed, the plane maintains a constant airspeed. We use the elevator to compensate for small deviations from stable, unaccelerated flight (and then use trim to reduce the amount of stick or yoke pressure necessary to achieve this goal).

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**Stability and Stall Recovery**

Several factors affect how an airplane will stall, especially weight and balance. If 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.

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**Stability and Stall Recovery**

Let’s assume the wing exceeds its critical angle of attack, 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.

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**Stability and Stall Recovery**

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.

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**Stability and Stall Recovery**

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 data must come from the documents specific to that airplane. These documents are required to be onboard the aircraft during all flights.

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**CG Loading Limitations**

Just how far ahead of the wing’s center of lift should the loaded CG be? That depends upon the downward lift available from the tail at various elevator deflections. For any plane, there are limits on how far forward, or back, the CG needs to be, and these vary with weight. A loading envelope helps keep us safe.

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**Plotting on the Envelope Diagram (1)**

Here is a typical weight and balance envelope. It comes from the approved flight manual (POH or AOI). Note that it lists weight along the vertical axis, and CG along the horizontal.

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**Plotting on the Envelope Diagram (2)**

The red polygon represents the range of acceptable values within which the total weight and CG must fall.

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**Plotting on the Envelope Diagram (3)**

First find the total weight on the vertical scale, and plot a horizontal line through it.

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**Plotting on the Envelope Diagram (3)**

Next, find the CG on the horizontal scale, and plot a vertical line through it.

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**Plotting on the Envelope Diagram (4)**

The intersection of these two lines represents the loading of your aircraft. It must fall within the red polygon representing safe values.

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**Plotting on the Envelope Diagram (5)**

Now, calculate the weight and CG for the end of the flight (fuel burned off), and repeat the process.

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**Plotting on the Envelope Diagram (6)**

Notice that the wt/CG dot has moved down and to the left. But, for a well-designed aircraft, the dot should still remain within the envelope.

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What Happens In Flight? Throughout a flight, the CG and weight constantly change. You must ensure that at no time do they go outside of the loading envelope.

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Review Questions In what unit are each of the following quantities expressed? Arm Moment Center of gravity Empty weight Payload Datum CG ref. MAC To determine moment, multiply ____________ by _____________ To determine CG, divide ______________ by ________________ What happens to weight and CG during flight? When may the wt/bal dot extend outside the envelope? Write down your answers before continuing to next slide

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Review Answers In what unit are each of the following quantities expressed? Arm inches Moment inch pounds Center of gravity inches Empty weight pounds Payload pounds Datum unitless location CG ref. MAC % To determine moment, multiply _weight__ by ____arm____ To determine CG, divide _total moment_ by _total weight_ What happens to weight and CG during flight? weight decreases, CG moves forward When may the wt/bal dot extend outside the envelope? NEVER! Review any missed questions before continuing to today’s flight.

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**Before Today’s Flight Determine your weight, and your instructor’s**

Measure fuel quantity and calculate fuel weight Weigh whatever’s in the baggage compartments Do a full Wt/Bal calculation, at takeoff weight Estimate flight duration and fuel burn Do another Wt/Bal calculation, at landing weight Go over these figures with your instructor Repeat before every Cross Country flight.

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