EASA MASS AND BALANCE MASS - measure of amount of material in an object, being directly related to the number and type of atoms present in the object - does not change with a body´s position - unit of mass is expressed in kg - also defined as inertial resistance to acceleration WEIGHT - gravitational force acting on a body - measured in Newtons (N) - weight is a force depending on the local acceleration due to gravity - thrust (=force generated by helicopter rotors for lift and propulsion) also measured in N - acceleration for calculation purposed on the surface of the earth: 9.81 m/s2 - relationship between force (F), mass (m) and acceleration (a) also known as Newton´s second law: F= mxa when dealing with weight, the letter F is often substituted with G, and the letter a is often replaced by the letter g (= standard gravity of 9.81 m/s2 as mentioned before) G= m x g weight of a body with a mass of 1 kg would be G = 1 kg x 9.81 m/s2 = 9.81 N Importance of Mass mass limitations due to structural reasons, exceeding result in structural overload and potential failure allowable masses for a certain flight may be lower, referred to as performance limited due to landing area (layout, elevation), air density, OAT and other meteorological conditions in general performance of helicopter will be affected by its mass Effects of excessive Mass the higher the mass of helicopter the more lift is required in any given maneuver (leading to an overpitch) the higher the mass the greater its inertia, both acceleration and deceleration will be more difficult Effects of too little Mass minimum permissible mass, usually related to the autorotation characteristics of (light) helicopters because too little mass may result in an inability to restore rotor RPM when entering an autorotation even with collective full down Center of gravity position of the center of mass abbreviated as CG, the point where a body is balanced three axes (pitch, roll, yaw) about which the helicopter rotates, intersect at the CG if body suspended from any other point, rotation until the CG is directly underneath the point of suspension influences the stability of a helicopter: - CG forward of limits dangerous as you may have not enough rearward cyclic authority to bring the helicopter to a stop or to flare at the end of autorotation - CG position aft of limits may result in impossibility to counteract the drift of a headwind due to limited remaining rearward forward cyclic as well as difficulties or impossibility to fly upper allowable speed range Conversions Mass 1 kg = 2.2 lbs Lengths 1 feet = 0.3 m Volumes (Liquid) 0.83 Imperial gallon = 1 US gallon = 3.78 liter Distances 1 NM = 1.852 KM Allowed take-off mass the mass taking into considerations all possible limitations for takeoff including restrictions caused by regulated takeoff and landing mass. Allowed takeoff mass = performance limited landing mass + mass of fuel used (trip fuel*) *amount of fuel burnt from takeoff to landing Helicopter Mass check - intervals not exceeding 4 years - assuming even temperature and being free from moisture, fuselage is longitudinally level - to measure mass and CG-position of aircraft, weighing with a minimum of 3 points of support is necessary 𝐴𝑥𝐵 𝐶 A: distance between front and rear reaction B: mass at nose C: basic mass Traffic load at MTOM the traffic load available will be: MTOM – DOM – total fuel = x at MLM the traffic load available will be: MLM – DOM – landing fuel = x at MZFM the traffic load will be: MZFM – DOM = x the limiting traffic load is the lowest of the three calculated x Center of gravity total moment (either negative or positive) of a force with respect to a given reference point is the distance from the reference point to a point where the force acts, multiplied by the component of the force normal to the line between the two points Moment = force x arm* when calculation in Newton *arm is known as perpendicular distance (d) from the line of action to the axis of rotation If calculations are made in terms of mass (kilogram) because standard gravity is omitted due to all masses in the example have been multiplied by 9.81 m/s2: Moment = mass x arm CG is found by dividing the total moment with the total mass. CG = 𝑡𝑜𝑡𝑎𝑙 𝑚𝑜𝑚𝑒𝑛𝑡 𝑡𝑜𝑡𝑎𝑙 𝑚𝑎𝑠𝑠 Corrections by moving loads 𝑤 𝑑 = 𝑊 𝐷 w: mass of cargo moved between two points W: total loaded mass of the helicopter d: distance that the CG will move D: distance between the two points that load is being transferred between If a correction by removing load is needed, we have to +/- the change in moments and use the new total mass in our formula. or m x D = 𝚫CG x T m: mass to be moved D: Distance of the mass to be moved Δ CG: change in CG T: total mass Sign convention for finding moments Mass: added (+), subtracted (-) aft of datum (+), forward of datum (-)? Aviation exam explanation CG position = Total moment ÷ Total mass Mass Definition Airframes, engines removable equipment unusable fuel, oil, hydraulic fluid variable load (crew, crew baggage, catering, optional equipment) Payload/ traffic load fuel Basic empty mass (BEM) Dry operating mass (DOM) Zero fuel mass (ZFM) Operating Mass (OM) takeoff fuel Take off mass (TOM) takeoff fuel Landing mass (LM) fuel remaining Remember 1 kg = 2.205 lb 1 m = 3.28 ft BEM + Crew and standard equipment DOM + TL + TOF OM ZFM F + TOF + TL TOM - TF + run-up / taxi fuel LM RM Calculating the change in center of gravity position change in total moment = change in moved mass moment M x 𝚫D = m x 𝚫d M: total mass of the aircraft m: the mass to be moved ΔD: distance between the previous and new center of gravity position Δd: distance between old and new position of the mass to be moved old total moment + moment of the ballast = new total moment (Adjusting formula for CG) and New total moment = old total moment + or – load shift Maximum allowable take-off fuel is the lowest of 1) regulated takeoff mass – zero fuel mass 2) maximum structural landing mass – (Zero fuel mass – trip fuel) Maximum extra fuel = maximum allowable take-off fuel – actual take-off fuel Index - the value of an index can be found if the moment is divided by a constant, usually 1000 index is used to simplify calculations by decreasing the value, therefore reducing figures manipulated by the user and representing the mass and the location of each item - Dry operating index (DIO) means the index for the position of the CG at the dry operating mass mass of load Running load in kg/m = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑙𝑜𝑎𝑑 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑙𝑜𝑎𝑑 surface load in kg/m2= 𝑙𝑒𝑛𝑔𝑡ℎ 𝑎𝑛𝑑 𝑤𝑖𝑑𝑡ℎ 𝑜𝑓 𝑙𝑜𝑎𝑑
