Performance By The Numbers

I’ve never bought into the idea that adding 20 lbs of ballast, or flying a glider at the top of the weight range will suddenly have you whizzing past your buddies at mind-bending speeds. Or even less likely, that doing either of the above will suddenly make un-flyable conditions flyable. And glide ratios? Not so much. Or rather, I don’t buy the rationale for getting excited about 0.5:1 differences. David Dagault mentioned the tiny differences in glide ratio in the February issue and his deductions about the compromise between safety and performance are spot on. But what are the advantages of adding weight, how do the numbers really work out and how do we get that 100% performance out of our gliders? This article will attempt to examine the mathematical realities, the huge effect that a little speed can have, and what that extra 0.5:1 glide really does for you. As a kid who nearly failed high school math I’ll try to make it as painless as possible. If, like me, a string of numbers makes your head hurt and you care more about the color of your glider than it’s glide ratio, skip it! If you’re still with me, I’ll try to pull back the curtain on the wizardry we call performance with a few examples and a bunch of numbers. Hopefully you’ll walk away from it relatively un-molested by numerology and with a new appreciation for your speed-bar.

Weight

It’s common knowledge that adding weight to an aircraft increases all the speeds including stall, min-sink, trim, and 100% speed-bar. Sailplane pilots commonly carry ballast during competitions or XC flights, small airplane pilots calculate extra weight into their takeoff and cruise speeds, competition HG/PG pilots have been known to toss on 10Kg, etc. The point is, speed increases with weight. For the examples I’ll concentrate on trim speed in a paraglider because it’s where most pilots fly their gliders most of the time and will illustrate the advantages and disadvantages with minimal trauma to the frontal cortex.

So, how much do we get? Adding weight increases the speed % by the square root of the % change in weight. If your weight doubles (2X weight increase) your speed increases by the square root of 2 or 41%. Sounds like a lot! Yes, but that was a tandem with a solo glider. Not terribly realistic unless you live in Europe and don’t mind getting wiped across the landing zone. For the rest of us, the reality is somewhat less astounding. If a 176Lb (80Kg) pilot adds 22Lb (10Kg) they’re going to increase their airspeed from 37 Km/H, to 39.2 Km/H. That’s about a 6% increase and it’s not exactly going to blow your buddies away at the local ridge site. It can add up but we’ll get to that later. I don’t know about you, but carrying around 22 Lbs of ballast gets old pretty quickly anyway. However, flying the next size smaller would put you higher in the weight range. The difference between flying at the top of the weight range, and the bottom is about 2.9 MPH or 4.6 Km/H assuming the weight range is 20Kg. That might be a deciding factor in choosing your next glider, but keep in mind that there’s also a performance disadvantage when flying a smaller glider. Your glider, you know, that thing providing lift, is smaller but your drag, mostly from lines and the pilot, remains nearly the same. Your Lift/Drag ratio takes a hit and you lose around .2 on your glide ratio (we’ll talk about what that means later too). As a general rule, for every 22 lbs you add, you can add about 2.25 Km/H or 1.4 MPH to your trim speed. The other speeds on your polar curve will increase by less toward the stall, and more toward 100% speed-bar, but always by the same percentage.

Your forward speed with extra weight, or by flying high in the weight range, isn’t the whole story though. Your vertical speeds will also increase. Not by much, but to use the same 22Lbs the vertical descent rate would increase by 6% or (assuming the glide ratio is 8.3) 30 fpm. It’s not a huge difference until you find yourself scratching for that weak chunk of lift that’s going to get you out of a tough spot or you’re ridge soaring on a light day. How often you find yourself in those situations is up to you. Interestingly, the amount you increase your sink rate is smaller at the top and bottom end of your speed range, but again, always by 6%. The result is a slightly flatter polar curve with extra weight. If the climb rates are good, and lift is aplenty the added 30 fpm is inconsequential to the vast majority of us.

To calculate your own speed with added ballast take the Square root of (New Wt./Old Wt.). Then multiply the result by your old speed. You can substitute your New Wt. for your current weight, and the Old Wt. for the middle of the gliders weight range which is where many manufacturers measure the published trim speed. Your old speed then becomes the published trim speed which will give you a good idea of how much you’ll gain by flying at various points in the weight range.

Glide Ratio

It’s not uncommon to hear aspiring XC pilots talk of stepping up to a “higher performance” glider. The oft quoted figure and rationale for a new bag-o-joy is the glide ratio. But is that really where we’re going to see the biggest advantage? Certainly it makes some difference but how much and in what conditions?

Since most of us fly DHV 1 through DHV 2 gliders we can generalize and use glide ratios of 8.0:1 through 9.0:1. Let’s start with the typical transition between a DHV 1 and a 1-2 and assume our DHV 1 gets an 8.0:1 while our 1-2 gets an 8.5:1 glide ratio. The speed is irrelevant at this point because we’re not dealing with wind or time. The arrival height difference between the two gliders, after a 1 Km glide, is 24 feet (or about 6%). That’s a distance you can make up for in about 7 seconds with a very light 200fpm climb. For reference, the distance between you and your glider is about 20 feet. If you’re worried about 24 feet after a one Km glide, a bad decision was made about 1 Km ago.

Most pilots don’t go cross-country. The vast majority of us are content to boat around with friends, enjoy the scenery, make it to the LZ, and have a beer. As such, most of us will never see more than a hundred foot difference between an 8:1 and an 8.5:1 glide. We shouldn’t be using “I just barely cleared those power lines in front of the LZ” as a rationale for a higher performance glider. There are other reasons for that new toy.

Cross-country pilots have to decide whether that 24 feet could make a difference. Are you already flying long XC flights with a 1 or 1-2? How close together are your connection points and how strong is the lift when you get there? If the lift is strong, and the connection points are close together, the arrival altitude will be of minimal importance and isn’t going to keep you from long XC flights. If the connection points are 10 Km apart, you’re now arriving 241 feet lower than your buddy on the 1-2. Still not that significant if the lift is strong, but it does start to add up. Over the course of a 40 Km flight you’d lose an extra 965 feet below the 1-2 but, be honest now, how often do most of us get the opportunity to put down 40 Km or more and would an extra 965 ft have gotten us there or was it a bad decision that put us on the deck?

As we step from the DHV 1-2 to a typical DHV 2 (9:1) our performance advantage is even less. We’re down to a 22 foot difference and that will continue to decrease as glider performance increases. As we stride into the next few decades, when gliders that most of us can fly reach 11.5:1, 12:1 and beyond we’ll be getting excited about arriving only 12 feet higher, or less!

This doesn’t mean that all gliders are created equal but in the small jumps we typically make between gliders, the performance differences aren’t going to blow your socks off. The difference between a DHV 1 (8:1) and a Competition level glider (10:1) is 82 feet after that same 1 Km glide. After 10 Km it’s 820 feet. Of course, if you’re not ready to fly a comp glider, you’re chances of making it past the first strong thermal with clean shorts is slim and your performance won’t matter much after that. So please don’t think I’m advising you to jump to a competition glider to get the most performance!

Speeeeeeed!

Speed is the oft overlooked performance figure and will bring us back to the weight relationship. How often have you heard “I’m stepping up to a glider with a 1 MPH faster trim speed”? Not very often. In fact, that’s where most of us are going to get most of our useful performance and can in some situations make up for a significantly lesser glide ratio. Some of you are now asking yourselves: “Isn’t this speed-to-fly?” Yes, but don’t spoil the surprise for everyone else!

For the first example, let’s look at 4 gliders, all of which get 8.5:1, which is irrelevant for this example but I include it to assure you that every glider arrives at the same altitude. There is no wind and the gliders are flying at trim. Glider A trims at 32 Km/H (20 MPH), B at 33.7 Km/H (21 MPH), C at 35.4 Km/H (22 MPH), and D at 37 MPH (23 MPH), which at the low end are modest speeds for most gliders but useful for this example. Glider A takes 1:52 minutes to fly a 1 Km course. Glider B takes 1:46, C does it in 1:41 and D in 1:37. Glider D is arriving a full 15 seconds before glider A over a paltry 1 Km course. That’s 13.4% faster. Over a 10 Km course it’s 2:33 minutes faster and over a 40 Km course, just over 10 minutes! This is why some competition pilots carry ballast. If you can increase your speed by adding 10Kg and picking up 2.2 Km/H from 35.7Km/H to 37 Km/H, you’ll arrive 3 minutes faster through a 40 Km course. On task 4 of the 2009 PWC, with a 84 Km course, 7 minutes made the difference between 1st, and 16th place. Certainly pilot skill and speed-bar use had a great deal to do with it, but gaining even 2 Km/H over the distances flown in an arena like the PWC can’t hurt. As a general rule, you can decrease your arrival time by about 4.5% for every 1.6 Km/H or 1 MPH you increase your speed.

Factoring wind into the equation makes the performance advantages of a faster glider even more apparent. Let’s now assume there’s a 16 Km/H (10 MPH) headwind. Those same gliders, A, B, C, D, are traveling the same 1 Km course, at trim and into the wind. Glider D is now arriving a full 0:54 before glider A and 92 feet higher because while the sink rate hasn’t changed, the amount of time glider A has been sinking at that rate is longer. This is where the numbers get interesting! If Glider B, rather than getting an 8:5:1 glide now only gets an 8.1:1 it will arrive at the same height as Glider A but do it 22 seconds faster. Glider C could get a 7.8:1 glide ratio and achieve the same altitude but 0:40 before glider A. Glider D could get a 7.5:1, arrive at the same altitude, and still do it 0:54 faster! That is the essence of Speed-To-Fly, and why a little speed-bar can make a big difference despite the sink rate/glide ratio hit.

To bring this full circle and back to the advantages/disadvantages of adding weight, let’s revisit that .2 you lose off your glide ratio by flying a smaller glider in order to be at the top of the weight range. You have the glider you want all picked out. It’s the PERFECT color but you can’t decide which size to fly. The small weight range is 60-80Kg and the medium runs from 80-100Kg. Naturally your all-up weight is 80Kg. Why does it always work out that way? The published speeds are 37 Km/H and 8.5:1 at trim for both sizes, but you know you’re going to lose .2 off your glide by flying the smaller size. You’ll be flying the small at 107% of it’s published speed, and the medium at 94% meaning that you’ll arrive at your destination 1 Km away 12 seconds earlier on the small. Because of the slightly lower glide ratio you’ll also arrive 9 feet lower. However, with just a 6 Km (3.7 MPH) headwind, you will begin to arrive higher than the medium, and 17 seconds earlier. Those performance gains will increase with greater headwind. The small glider, in those conditions or into any headwind greater than 6 Km/H, will perform better.

To be clear, none of these numbers are a reason to get a tiny glider so you can fly a ridge site when it’s blowing 20+ MPH. It’s essential to consider your safety margins and those margins should be large enough that the difference in speed between the top and bottom of the weight range is inconsequential to the conditions you’re flying in.

Density Altitude

We know from our basic training that the atmospheric density decreases with altitude and barometric pressure, and with an increase in temperature. By factoring in those three components we can get our Density Altitude or the altitude at which it FEELS like we’re flying. For the purposes of our example I’ll leave the standard atmospheric pressure at 29.92 and the temperature at the standard 15ºC. At 10,000 ft, in standard conditions, it feels like we’re at 10,000 ft but If the temperature rose, or the barometric pressure dropped, we’d feel like we were at some altitude higher than 10,000 ft. But why do we care? Because speed increases with higher density altitudes! In small aircraft the Density Altitude is used to calculate takeoff distances, speeds, cruise performance, etc. and the same applies to us. Anyone who has flown Aspen or Telluride can tell you that takeoff is longer, speeds are higher and we can calculate by exactly how much. For every 1,000 ft in Density Altitude, we increase our speed by roughly 1.5%. Doesn’t sound like much until you’re at 10,000 ft in the Owens, Aspen, Snowbird, Valle De Bravo etc. and you’re tripping along 15% faster than you were at sea level (horizontally and vertically). You’ve heard the adage “get high, stay high”? This is one of the reasons why, aside from the fact that you have options at altitude. A 15% increase in speed is nothing to scoff at. If you trimmed at 37 Km/H at sea level, you’re now trimming at 43 Km/H! Remember how even a relatively small difference in speed can make a significant difference in arrival times? Now you hit the mother-load in the Owens and get the wild ride to 17,999, right to the floor of Class A airspace. That’s a 28% increase and you’re trimming at 49 Km/H true airspeed (not indicated). Alternatively, if you’re flying a glider that trims 1.6 Km/H (1 MPH) slower than your buddy, you’d have to fly ~3000 feet higher just to keep up. So for those of you who get high and go far, staying high has advantages well beyond options and the view.

To calculate the Density Altitude, ignoring moisture content which has a relatively small impact, you can use the equation: Altitude + ((29.92 - Baro Pressure)*1000) - ((15 - Temp ºC) * 120).

Drag

Since most glider manufacturers measure performance with aerodynamic harnesses, the rest of us are forced to wonder what exactly the drag off an upright harness is costing us. The answer is pretty simple. An upright harness will typically cost you 2.4 Km/H and 0.9:1 off your glide ratio or 7 seconds and 46 feet over a 1 Km course. That’s an altitude difference you can make up for in 14 seconds with a 200fpm climb, but you’ll never be able to make up for those 7 seconds and that 14 seconds you had to waste getting your altitude back will catch up with you if you’re going cross-country in a race against the sun. All accounted for you’ll be 21 seconds behind your buddy with the same glider but an aerodynamic harness after just 1 Km.

While we’re on the topic of how manufacturers measure performance, most of them gather polar data at 1,500 Meters or 4,921 feet above sea level. You can knock roughly 2.7 Km/H or 1.7 MPH off your speeds if you’re boating around at the beach.

Reality

But enough of this hypothetical stuff. Let’s look at the full range of gliders from Advance in the 28 sq meter size with an all-up weight of 97.5Kg. Their current range consists of the Alpha, Epsilon, Sigma, and Omega. Gotta hand it to the Swiss for being consistent with the their naming schemes. I chose Advance for the example because most of their gliders have been refreshed within the last year, they were very generous with polar curve data, and they have a nifty Speed Performance Indicator right on the back of their risers that will help pilots get the most performance. They know how much speed matters and they want us to know too. Kudos to them for making it easy for us.

Table A

Table A shows polar curve data for 4 points for all 4 gliders (min-sink, trim, 50% bar, 100% bar), their weight range, the pilot’s weight, the polar curve data corrected for a 97.5Kg pilot, the weight range and the percentage of the published speed you’ll get from the glider at 97.5Kg. I left out the range between min-sink and stall because nobody interested in performance, or self-preservation for that matter, flies around that slow. Table B shows the test distance, the published L/D ratio of each glider, the weight-corrected trim speed, and the glide ratio corrected for wind which is 0 for this example. It also shows the altitude lost along the test distance, the altitude above the lowest glider after the test distance, the time to complete the test distance, and the speed & glide % advantage over the glider that had the lowest respective altitude, or greatest time at the end of the test distance. I’ve left the numbers uncorrected for Density Altitude to keep things simple. What we can glean from the pile of numbers is that we’d be flying the Alpha at 103% of it’s published speed, and the Epsilon at 100% of it’s published speed. The result is that the Alpha arrives at goal 1 Km away 2 seconds before the Epsilon, but 26 feet lower. Not bad for a glider with a 0.6:1 glide ratio deficit! Most of us would swoon over picking up 0.6:1 on our glide. As we step up to the Sigma we see that we will arrive 2 seconds before the Epsilon, and 10 feet higher. The Omega will arrive another 2 seconds earlier and 26 feet higher than the Sigma but we’re only flying it at 97% of it’s published speed so we’re not getting all the speed we could out of it. As I’ve mentioned before, these values do add up, sometimes significantly over greater distances or into a headwind, but most of us are not reaching those distances anyway, due either to lack of desire, skill, or conditions and if we’re attempting to lay down some miles we’re not going to try to do it into the wind. With a tailwind the performance differences decrease to a point where, with a 30 Km/H tailwind, 34 feet separates the Omega from the Alpha instead of the 62 foot separation in nil-wind conditions.

Table B

We could go on to compare gliders with 0.5 MPH speed differences and 0.2:1 glide ratio differences, but we already know how small the differences are with larger numbers. Calculating your own arrival time is easy enough. Time=Distance/Speed. Calculating the altitude lost is equally straight forward. Altitude Lost=(Km Flown*3280.8)/Glide Ratio. Plugging in your weight-compensated speed might help you decide whether you want to be heavy on the small, or light on the medium.

To wrap up the performance examples, let’s look at a short cross-country flight of 20 Km, with a 500fpm climb at the end. Both gliders get 8.5:1 but glider A trims at 37 Km/H and glider B trims at 39 Km/H. Glider A arrives 1:39 seconds behind glider B but at the same altitude. Glider B can use that extra time to climb 832 feet before glider A has even arrived.

Now we can do the same flight with 2 different gliders that have the same trim speed of 24.25 but glider C has an 8:1 glide ratio instead of the 8.5:1 that glider D gets. At the 20 Km mark glider D arrives 482 feet higher which would take glider C 58 seconds to catch up to in a 500 fpm climb

Finally we can do the flight again with gliders that have different trim and glide ratios. Glider E trims at 39 Km/H but has a glide ratio of 8:1 while glider F trims at 37 Km/H and gets 8.5:1. After the same 20 Km glider F arrives 482 feet higher, but 1:39 behind. That's time that glider E can use to climb 825 feet giving it a 350 foot altitude advantage by the time glider F arrives. Suddenly thinking about using that speed-bar more often? Me too.

Remember that all three examples were over 20 Km and the difference we’re talking about is still relatively small.

Up until now, we’ve completely ignored pilot skill, glider handling when heavily loaded vs. lightly loaded, and the associated difference in DHV/EN test results. We’ll keep it that way. Those are differences that get hashed out in places like Valle De Bravo, the Owens Valley, and the Alps by pilots with names like Russell, Torsten, Christian, Alex, and Jean-Marc. I won’t pretend to be able to tell you which glider to fly, where in the weight range or in what DHV category. Those are decisions you’ll have to make based on the conditions you fly in, the kind of flying you’re doing and the amount of passive safety you want from your glider. Hopefully the numbers have convinced you that you don’t absolutely need a hot-ship to go places and that a little speed-bar can make a big difference in your performance, even when you’re taking a typical DHV 1-2 up against a typical DHV 2. Don’t let the small differences in performance on paper discourage you from a new glider either. Newer gliders do have better performance, they’re generally safer and if you like the handling, you will fly better. The equation for calculating the performance of a glider you actually enjoy is: ((Speed/Glide)^fun) + pretty colors.

For the spreadsheet that was used to generate all the figures, go here. Using Apple Numbers 2.0 you can enter your own polar curves, altitudes, weights, and compare performance figures. It will also generate a Hoisington Chart (so dubbed after Zach’s 2005 Woodrat Speed-To-Fly presentation) that can be used in flight to maximize performance.

Hoisington Chart

(Red gliders and helmets with flames on the side will increase your speeds by roughly 5%.)