when we're flying along the cruise we need to be able to calculate how much more distance we can cover with the amount of fuel that we have in our tanks otherwise we might run out of fuel halfway along our journey but how do we calculate this figure let's find out [Music] hi I'm Grant and welcome to the eighth class in the performance Series today we're going to be taking a look at range which is basically a measure of efficiency range will dictate how far we can fly for and which airports we can visit so it's important to understand how we calculate the range for the fuel that we have on board or the maximum amount of fuel we can put in the tanks specific range is the distance an aircraft flies through the air per unit of fuel used if we add in the effects of wind we get the specific ground range the distance we actually cover over the ground rather than through the air because wind will cause the parcel of air that we're flying in to move along the ground as we're flying through it think of it like we're flying inside a big train if the train is stationary we just fly to the end of the train but if the train is moving we'll fly to the end of the train but the whole thing has moved to our position relative to the ground will be different if there is no wind think of the train being stationary then our specific range are and our s uh our specific ground range sorry will be the same the units for specific range will be nautical miles per kilogram of fuel used and if we divide by time we can get two formulas one for a specific range or one for a specific ground range the one for a specific range the air distance would be the true air speed over fuel flow and for ground range we just need to factor in wind and we can do that by using the ground speed which is the Tas plus or minus any wind component and then divide that by the fuel flow as well depending on the conditions we are flying in we need a certain amount of thrust that we need to overcome all of the thrust required or the drag that is produced when we fly thrust generation requires us to use up Fuel and how much fuel depends on the specific fuel consumption of the engine this is basically a measure of engine efficiency and it is the amount of fuel flow needed to produce one unit of thrust in a jet aircraft and a propeller it's the amount of uh fuel used to produce one unit of power why is this important though well we already have a formula for a specific range in specific ground range but we can break down the fuel flow into a little bit more detail if we first have a look at the jet aircraft then we can substitute in the value for specific fuel consumption into the specific range equation and get specific range is equal to the true air speed over the specific fuel consumption times drag or the amount of thrust required for that phase of flight or if we want to find the specific ground range we just have to substitute in ground speed for a propeller it is slightly different the difference is that bottom line where we have to have the consideration of specific fuel consumption per unit of power so we get the same equations but on the bottom line it's power required at that phase of flight so why have we substituted in those values for instead of fuel flow basically well it basically allows us to see a bit more clearly the factors that affect fuel flow and our specific range so if we look at this one for example we know that if the specific fuel consumption is high and the drag is high that means that we're going to be dividing by a larger number and that means our specific range is going to go down if we take the specific ground range of the propeller for instance if we have a low specific fuel consumption and a low amount of power required we're dividing by a small number which means our ground range is going to be high it's just an easy way to analyze range is influenced according to a number of factors most of them you can figure out by looking at the equations that we've just worked out but first we're going to have a look at Mass if we compare a light aircraft to a heavy one the total drag curves look like this mainly because heavier aircraft need to produce more lift a more induced drag is generated result this means that on the lighter aircraft the drag is lower when we fly at the speed for max range which now I think might have not actually talked about the speed for max range so let's just do a little sidebar here so max range is called VMR or if you're flying at Mach numbers m m r speed Mach number and it occurs where we maximize our thrust to drag ratio and in a turbo jet or a jet in general this occurs at 1.32 vmd and this is the tangent on this curve so if you go somewhere like that this value here is our VMR which will be 1.32 vmd in a propeller driven aircraft we take the tangent to the power curve not this drag curve and it's the same effect we're maximizing our thrust to drag or Thruster power required um ratio and this actually occurs therefore at 1.32 VMP speed for minimum power which coincidentally is actually vmd because the speed for minimum power is 0.76 vmd and 0.76 times 1.32 equals close enough one so it's therefore equal to the speed for a minimum drag so what was I saying yes lighter aircraft um have less drag basically and if you look at the equations for both turbojet and propeller aircraft the bottom line has dragging it or power required which is essentially drag type speed so if you have a lower amount of drag that means you're dividing by a smaller number which means your specific range goes up simple as that and also take note that if we are um lighter or speed for VMR would be a bit slower as well so that would be VMR in the heavy aircraft and then as we get lighter our speed slows down same for the propellers if an aircraft is flying at its Optimum altitude the range will be maximized this Optimum altitude in a turbojet is high up basically the engines are running at their designed RPM because they're designed to cruise because that's where they spend most of their time and that's where they are most efficient making the specific fuel consumption low and also upper altitude the air is less dense meaning drag is lower so our specific range goes up on our specific ground range will go up as well in a propeller driven aircraft the optimum altitude isn't as simple as it depends on throttle position and propeller RPM combinations and Optimum combinations and altitudes are often tested out and put in manufacturer's manuals so it's hard to see but it's not going to be quite as high up but it's going to be the position for basically maximum throttle open so altitude and mass are the two biggest influencers on commercial flights so this is an example of a step client it's something you see quite often so say we first reach our cruising altitude of 30 000 feet we're heavy and full of fuel and as we Cruise along we burn fuel and weight as a result this means our drag reduces because we're needing less lift and therefore the specific range increases which is good we're lowering our drag specific range goes up this reduction in Drag and a lower um speed for maximum range requires less thrust to be used so the engines don't have to work as hard so the RPM of the engine of the route can reduce this means that the engine May no longer be operating in its ideal range which is typically um around 90 to 95 so we counter intuitively want to make the engines work a bit harder again to get them back into this efficient range we do this by climbing into less dense air meaning more air has to pass through the engine in order to generate the correct amount of thrust and the engine has to rotate faster as a result pushing us back up into the ideal RPM range this means that throughout the flight our Optimum altitude to keep the engines working in the efficient 90 to 95 range steadily climbs as we go throughout the flight as we burn weight in practice though we can't slowly climb along as we fly because if everyone's doing it there'd be a ridiculous number of collisions in the air so what we do is we fly at one altitudes 30 000 feet at the start maybe slightly above the optimum altitude then as we burn fuel the optimum altitude will climb up to meet us then pass through our level once it reaches a thousand feet or so above we would request to climb up to the next level 32 000 feet then again it would climb up to reach us and so on and so forth throughout the flight um until we reach the structural limit of the aircraft this is known as a step climb and it's something you do almost every flight when you're flying commercially just to save fuel by flying as close to the optimum altitude as possible so wind influences the specific ground range but not the specific air range the specific range is the specific air range but it's just called specific range so basically it's because Taz and ground speed while Taz isn't affected by wind and ground speed is equal to Taz plus or minus whatever wind component you've got so obviously the wind has an influence on this specific ground range but nothing to do with the specific gear range so if we add a Tailwind our ground speed goes up and our specific range wouldn't change but the specific ground change would go down as a result wait did I say Tailwind if it's a Tailwind it would go up if it's a headwind to the specific ground range will go down so that's how we get our maximum range out of an aircraft but it does require us to fly at MMR or VMR which might be a bit slow to get to our destination on time to pick up more passengers or pick up some cargo Etc so there's a commercial element we need to think about for this there's a speed generated for using um during the long range cruise and it's called vlrc this is a speed that's slightly faster than the speed for max range so there is going to be a bit more fuel burn but it's calculated so that you get um about four percent speed increase with about one percent fuel burn reduction or reduction range fuel burn increase and companies use this as a bit of a trade-off and there's also a speed which is called um the econ to be honest they're very rarely going to be V speeds they're going to be Max speeds and the way we figure out the econ speed is by using the cost index the cost index which I talked about briefly in the class before is usually in a range between 1 and 50 from at least at least from what I've seen anyway you could get higher I don't know Boeing an Airbus both use it but I'm not sure about other manufacturers and it's basically a trade-off between speed of flight and amount of fuel burn if you have a really low cost index you'd save a lot of fuel but fly really slow and a high cost index would be the reverse fast flight burning lots of fuel we're given this cost index by the flight panning Department depending on how fast they need us to fly to arrive on time According to some timetables or slots or some other airports we then pop it into a computer on the aircraft and a Mach number for econ in the cruise our econ speed is generated and that's what we fly through the flight okay so a specific air range or the specific range is the two air speed divided by the fuel flow and the fuel flow is specific fuel consumption times drag for a jet and for propeller it is specific fuel consumption times power required think of drag as thrust required maybe that might help and if you want to convert them into specific ground range you just need to factor in the wind and to do that you just convert the tires into a ground speed because ground speed equals Taz plus or minus any wind component that's helping you this the speeds for max range speed MMR is going to be 1.32 times vmd that's basically the tangent to the drag curve where our thrust to drag ratio is maximized need a propeller it's slightly different it's tangent to the power required graph and and the tangent again means our ratio of thrust power required is maximized and that occurs at 1.32 VMP which just because the maths happens to be VMT VMT v m d sorry um yeah because VMP is 0.76 times vmd and 0.76 times 1.32 is basically one so things that influence our level of range our range specific air range for example is influenced by mass if we have more mass it means we have more drag and we have more drag we need more thrust which means our specific fuel consumption goes up and that means that well our specific fuel system option doesn't go up we just need more thrust but anyway has the same effect of reducing our range altitude for a jet basically means that we're operating in the ideal zone for our engines and the drag is lower meaning the specific range goes up in a propeller aircraft it's a bit different you basically fly at what the manufacturer has tested and found to be the most efficient wind has no influence over the specific air range but it obviously has a huge impact on the specific ground range because Tas plus or minus wind equals ground speed if you have a headwind you would have a lower ground speed and that would mean a lower specific ground range for example the speeds that we fly if we have MMR we're going to fire a max range that's going to be the best for us and if we fly at long range Crews we're getting four percent faster for one percent reduction in range a bit more fuel burn and normally we fly at M econ speed which is according to the cost index that range of 1 to 50 and telling us how fast to fly um and how much fuel to burn