if we have to hold near an airport because it's very busy with traffic or there's some weather passing through we need to know how long we can stay in the air for before we have to divert and land immediately so we're going to take a look at that in this class and figure out how to calculate our endurance [Music] hi I'm Grant and welcome to the ninth class in the performance Series today we're going to be taking a look at endurance endurance is how long we can stay in the air for and it's essentially another measure of efficiency just like range was in the previous class there are a few subtle differences between the two so it's important to understand range as well as endurance so you don't get caught out in the exam or indeed in the real world the time that an aircraft can stay in the air is known as endurance and to maximize our endurance we basically need to minimize the fuel flow into the engines and therefore the fuel burn in the engines this means that endurance is inversely proportional to the fuel flow because if we have more fuel flow we have less endurance inverse proportions we also can think of the fuel flow in terms of specific fuel consumption times thrusts required or drag which is how much fuel we use per unit of thrust that we need um at that time in flight and the thrust required sorry is equal to the track we can therefore make an equation for endurance that looks like this so endurance varies according to one over specific fuel consumption multiplied by drag and notice it's not the equal symbol and but it's the varies according to this is because it's not as simple as that and we need to consider a few other factors which we're going to have a look at so if we think about the speed that we would um need to fly to stay in the air for the longest possible time to have maximum endurance we have to have a low specific fuel consumption and drag and the lowest amount of drag we can have is when we're at vmd that's for a jet propeller endurance is very similar but because we're talking about propellers fuel flow is equal to specific fuel consumption times power required this means our equation becomes endurance varies according to one over sfc times power required and again we can see from this equation that the speed for endurance to be maximized would be where we have a lower specific fuel consumption and a low amount of power required which occurs at VMP when we're flying in a propeller a few things will play a role in endurance which is why our equation is only vary according to rather than equal um to get the lowest amount of fuel flow mass is the first of these influencers if we think about the drag and power curves we can see why a heavier aircraft basically needs more lift therefore producing more induced drag as a result this means that we have a drag curve which is further up into the right and it would be the same thing with the power required line this means to fly that to fly at the speed for best endurance vmd we need to fly faster and by flying faster we need more thrust which burns more fuel as a result it's the same thing for propeller there is more power required so we need to spin the propeller faster and have the engine going at a higher RPM and we therefore burn more fuel for any mass changes there's a cool estimation trick we can use for the questions and if we're flying at the correct speed if we're flying at vmd or VMP because at that point the variations are proportional because basically if we go slower or faster we get more drag um but basically yeah it's a new old equals new overall so new Mass over old Mass equals new fuel flow over old fuel flow and it can be quite useful in exams to gauge an estimation and let's have a look at an example an aircraft is holding overhead Gatwick at a flight a height of 3000 feet its mass is 50 000 kgs and it has a fuel flow of 2400 kilograms per hour if the aircraft holds for 30 minutes what will the new fuel flow be and then you could use that to figure out sort of endurance calculations so we'll write down our equation Nu over old equals new over old this will be Mass over here and fuel flow FF over here so our new mass is going to be half of the fuel flow because we're burning that's kilograms per hour we're only going for 30 minutes so our new mass is going to be 50 000 minus 1200. over the old Mass which is 50 000. and our new fuel flow is what we're trying to figure out our old fuel flow is 2400. so that is um 48 800 over fifty thousand equals n over 2400 rearrange that 48 800 times 2400 over fifty thousand equals our new fuel flow which if you put it into a calculator equals 2304 it's not exact but it's a good estimation so you know that as we get lighter we're going to burn less fuel that sort of adds up returning to the influencers then altitude is an important one to think about so the best altitude for endurance is where we have the lowest specific fuel consumption and in a jet that's where the engine operates in its designed RPM usually about 90 to 95 percent of the maximum this occurs normally at a high altitude because the engines are working hard to force enough massive air through the engines and engine designers choose 1995 for efficiency because this is where the jet spends most of its time in the cruise up high so it sort of makes sense in practice though when we're thinking about endurance it's normally when we're holding near an airport which means we're very unlikely to be doing that up a nice cruising altitude so for a jet aircraft the endurance is reduced as we're lower down because we're not going to be operating in this um ideal range so as alt increases the specific fuel consumption goes down and the drag would also go down meaning the insurance goes up and then if you flip that as we get lower we're going to burn more fuel it's going to get more drag it's actually quite significant on Jets how much your endurance is reduced when you go down to lower altitudes for a propeller it's slightly different if we're up high the power required curve moves up and to the right this is because if we're higher up in less dense air we need to fly faster in order to produce the same amount of lift as lower down and the speed for best endurance VMP is higher and that's a higher amount of power required so power required goes up if we go up in altitude which means that we're going to get lower endurance as a result so it's the opposite to a jet if we're lower down we're going to be flying at a slower speed for VMP our endured speed which means we need less power required and that means our endurance goes up so wind does not influence our endurance this is because we are thinking about distances along the ground uh just time in the air a strong headwind might slow us down across the ground but that doesn't matter if we're in the hold we're near the airport and as long as we can stay up in the air for 20 or 30 minutes it doesn't really matter if we're covering x amount of distance on the ground we just are interested in how long we're going to spend in the air in summary then I think of ranged endurance as being both sort of measures of efficiency they're very closely linked and there can be possibility to confuse them both just think of range as distance endurance is time and then you should hopefully be able to work it out and another thing I like to think of is jet equal drag prop equals power PNP prop isolated with power required so if we think about range for a second a bit of a Refresh on the previous class so the equation for range is either the truer speed or the ground speed if you're thinking about specific ground range over the specific fuel consumption times drag which is just the fuel flow the speed we need to fly is 1.32 vmd the tangent to the drag curve where our ratio of um thrust to drag is at its maximum the altitude that we get the best range is up high and if we think about a propeller it's the same equation except we're substituting in power required instead of drag the speed for that is at 1.32 VMP which just so happens to be the speed for minimum drag and the altitude depends on the manufacturer's design but it's basically where we have the throttle open so in today's class move to endurance which varies according to one over the specific fuel consumption times drag for a jet aircraft and we basically want to have the least amount of drag which is why we fly at vmd and it's also why we fly up high the second reason flying up high is that's where the engines are supposed to be um sorry that would be the other way around that's where the engines are supposed to be flown at so they're flying in a very efficient range of speeds RPMs for propeller again we're just substituting in power required and we want to basically fly where our power required is the lowest that'll be VMP and if we are high up in altitude or if we're lower down sorry that means our drag curve moves down into the left so our speed at the bottom of that curve will be lower requiring less thrust and um less power sorry and therefore we get a better endurance as a result foreign