Contents

• INTRODUCTION
• IMPROVING GLIDE BETWEEN THERMALS, NOT SPEED
• A BETTER BEST GLIDE
• GLIDES AT HIGHER SPEEDS
• THE GLIDER POLARS
• SUMMARY
• WHAT DO YOU NEED TO FLY S2F?
• DETAILS OF THE ANALYSIS

INTRODUCTION

Does the discussion of Speed-to-Fly bore you to tears? Before you yawn and turn the page consider this: If someone told you that you could improve your glide angle by 10% would you be more interested? How about if you heard that 15% glide speed improvements could be had? If you are an XC or race pilot then you are probably paying more attention. The main purpose of this article is to demonstrate that speed-to-fly is important for all XC pilots of hang gliders and paragliders, not just the competition pilots.

Using Speed-to-Fly (S2F) techniques has long been known to be useful to racing sailplanes, but in hang gliding and paragliding it has often been thought of as unnecessary. S2F is starting to penetrate the consciousness of hang glider pilots, but it is still considered too much work for too little gain. In paragliding the general belief is that S2F will not work because the speed range is too low. Now is the time to dispel these thoughts: Using S2F is easy and paragliders benefit greatly. If you fly XC or compete in hang gliders or paragliders, read on.

This article answers the question, "In a real flight, what does S2F do for me?" The unique aspect of this article is that it uses S2F analysis to demonstrate improved glide rather than improved speed. This is done by starting two pilots at the same height and at the same time , flying them on a long glide through the same air , both arriving at the next thermal at the same same time . Starting and finishing at the same time means that they both fly at identical average speeds. One pilot is flying speed-to-fly (S2F) and the other flying at a constant speed. The results are startling. In air where the overall up and down movement sums to zero, the speed-to-fly pilot out performs the constant speed pilot by large margins, specifically:

I think that most of us understand that these are significant numbers, but let us put them into perspective. Since the first Morningside Glide Ratio contest in 1988, glide angles have improved only 1.5 - 2.4 points, depending on how you look at the results. The average glide angle (as reported in the articles in Hang Gliding) of the top three gliders was 10.5:1 in 1988, as compared with 12.9:1 in the 1993 contest, a 2.4 point gain. Dennis Pagen states in his article on the 1993 contest that the 12.9:1 figure is probably high and true glide angles are around 12:1, meaning only a 1.5 point gain. By not using speed-to-fly then you are throwing away most of the glide angle improvements made in the last 5 years. Or even worse, a pilot who does use speed-to-fly may out glide you in a 5 year old glider!

Here are the results of the analysis for paragliders:

For paraglider pilots this is interesting news. The general belief is that the speed range of paragliders is too narrow to be able to use S2F. That doesn't mean that a paraglider doesn't have an optimum speed. True the improvements are not quite as large as for hang gliders, but 3 - 11% improvement is hard to come by any other means!

IMPROVING GLIDE BETWEEN THERMALS, NOT SPEED

The key element to this analysis is that it compares two pilots gliding from the top of one thermal to the bottom of the next in exactly the same amount of time. Unlike the usual speed-to-fly analysis, I do not want to find out who arrives there the fastest, but who arrives there the highest. Even though I do not care how strong the next thermal is, I do use different speed ring (aka MacCready) settings to see how the settings affect average speeds and glide angles. For those of you who believe that the speed-to-fly theory is only for racers, this article should convince you that speed-to-fly is also useful for anyone interested in better glide angles.

The air that these two pilots fly through has zero average vertical movement. That means that sometimes it's going up, sometimes down, but overall it adds up to zero. I also created two other parcels of air that have average vertical movement of +.25 m/s and -.25m/s (.25m/s = 50fpm.) In these two cases the air is actually slowly rising or sinking, respectively. The profiles of lift and sink for these parcels are shown in Figure 1 . Note how little difference in appearance +/-.25 m/s makes. (This segment of air was recorded on a barograph in the 1993 Owens Valley World Championships (Figure 6) .) Later on we will see how much difference the air mass can make.

A BETTER BEST GLIDE

Figures 2a & 2b show the glide paths of the two pilots along with the speeds flown by each for hang gliders ( Figure 2a ) and paragliders ( Figure 2b ). In all flights the two pilots are flying identical gliders at the same wing loading. In the flights of Figures 2a & 2b the air mass average is zero and the speed ring setting of The S2F pilot is zero. The S2F pilot and The constant speed pilot exit a thermal and start on a glide for the next. The S2F pilot flies using a speed-to-fly variometer (see side bar "WHAT DO YOU NEED TO FLY S2F?") which enables her to fly the optimum speed, and the constant speed pilot just flys at one speed. In the hang gliding example (2a) the constant speed pilot's speed, which is a constant 43.3 kph during the glide, is the same as The S2F pilot's average speed during the glide, i.e. they both arrive at the next thermal at the same time. Table 1 shows that The hang gliding S2F pilot gets 1.8 points and the paragliding S2F pilot gets .8 points better glide than their constant speed counterparts!

Most pilots do not vary their speed any where near as much as the speed-to-fly theory suggests. The speed plots of the S2F pilots in Figures 2a & 2b show that the deviation from the average speed is considerable. Remember that a speed ring setting of zero is for best glide, yet Figure 2a shows that speeds approaching 60 kph (43 kph for the PG) are required if the sink is strong enough. I think most pilots know to "slow down in lift and speed up in sink", but do you vary your airspeed anywhere near as much as The S2F pilots do in Figures 2a & 2b ?

GLIDES AT HIGHER SPEEDS

I next consider what happens if you want to achieve higher average speeds. This is done by increasing the speed ring setting: the higher the setting the faster the average speed. You will recall from your basic speed-to- fly theory that the stronger the next expected climb (the ring setting, according to the theory) the faster you want go to get there. Using a higher speed ring setting forces you to fly a little faster. Figures 3a & 3b show our two pilots flying through Segment 1 with three different speed ring settings: 0, 1.3 and 2.5 m/s. As expected The S2F pilot out glides The constant speed pilot every time, but look at traces 1b and 2a: The S2F pilot flying at a speed ring setting of 1.3 out glides the constant speed pilot who is flying at close to his best L/D speed and she beats him there by 1.79 minutes in the hang gliders or 2.2 minutes in the paragliders! (See Table 1 (HG) or Table 2 (PG) .) Is it starting to become apparent that paragliders can benefit from S2F?

Tables 1 (HG) and 2 (PG) summarize the results. Each table shows the L/D achieved by The S2F pilot, how many L/D points she beat The constant speed pilot by, and what their total time and average speeds were for three speed ring settings and three different average air mass movements. For example, the first box in Tables 1 (HG) & 2 (PG) summarizes what Figures 2a & 2b show graphically. The top row of boxes in Tables 1 (HG) & 2 (PG) summarize what is shown in Figures 3a (HG) & 3b (PG) .

The limited speed range of paragliders does have an effect on how high a speed ring setting will be useful. Figure 5 shows the effect of a low top speed, constrained by saftey and not performance. Low speed is relative to the polar. The optimum speeds in big sink at high ring settings are well past the safe limit. This graph shows that a speed ring setting of 2.5mps (500fpm) will push the pilot past the redline. As paraglider speeds increase, higher ring settings will become more useful. Table 3b shows the speed limits used in this analysis.

THE GLIDER POLARS

Table 3 shows the glide polars in parabolic form used to make this analysis. Figure 4 shows the polars graphically. These polars are representative of modern gliders, however not very accurate. By that I mean that the accuracy of the measurement techniques used is not good enough to distinguish between different makes of high performance gliders. They are accurate enough for S2F, and have been used for a long time in the Tangent with good results.

SUMMARY If you are a "boater" you stand to gain the most. By boater I mean you like to fly around in no great hurry, conserving as much altitude as possible. The tables show that big gains can be had, especially if there is a slight bit of upward movement in the air mass, such as underneath a cloud street or flying along a mountain range with a prevailing wind rising up it. The tables show that the improvements aren't as great if you are trying to achieve higher speeds. Thus, if you are a racer then you stand to gain less, but racers are possessed by the desire to improve performance by every possible means. It should be noted that a speed ring setting of 2.5 m/s is higher than I normally use, except when blasting up the White Mountains in the Owens on a very strong day, or when I'm coming in too high to goal. .5 to 2 is the usual range I use, even in the desert.

The results shown here represent the best possible improvements. Most pilots probably do not hold a constant speed, but do actually speed up and slow down some in sink and lift. Likewise, it is probably not possible to fly at the exact optimum speed all the time. If you are like most pilots who haven't paid much attention to speed-to-fly, you do stand to improve your performance by close to 8 - 10% when trying to achieve your best glide. Yes, it does take some effort on your part to start using speed-to-fly, however new instrumentation is making it easier. You work hard all year to afford the latest high performance ship, why throw that performance away?

WHAT DO YOU NEED TO FLY S2F?

My inspiration for using speed-to-fly came from flying against people like John Pendry and Larry Tudor. These guys had somehow figured out how to glide intuitively. Pendry's glide in Brazil one year was so good that it prompted one of his team mates to comment that he had "sold his soul to the Devil". I knew there was no way I was going to figure it out intuitively, in part because I do not get anywhere near the air time these guys do, but mostly because I think only a very few pilots in the world are capable of doing so. My only choice was to use the speed-to-fly theory.

How do you fly speed-to-fly? There are several methods. Thomas Suchanek uses a set of tables taped to his upright that he refers to and interpolates in his head. We should all be glad that he spends his time with his tables because it is frightening to consider what he would be like if he had an automated S2F method. Speed rings are the traditional method for hang glider pilots to implement speed-to-fly theory. If you have gone to the trouble of making one, you know that they require even more effort to use. The vario needle is constantly moving around, so if you are not constantly looking at your vario you do not know if you are flying at the correct speed. When you are gliding you should be looking ahead for clues about where to find your next thermal, not at your vario. In addition, a speed ring is only valid at one altitude and at one wing loading, and it cannot account for head or tail winds.

To facilitate S2F you need an audio indication to tell you to speed up or slow down so you can concentrate on the terrain ahead. You also need to have the audio for climbing. The least confusing way to do both is to have the vario automatically switch between climbing and gliding audio.

Enter the Tangent Flight Computer...

The Tangent Flight Computer is not a new concept. The sailplane community long ago devised the speed-to-fly vario. What is new is the complete S2F implementation for the free flight world. The TFC is the only HG/PG instrument designed around S2F from the ground up. The concepts in the TFC are based on my 21 years in hang gliding and experience in XC racing going back to 1978, in addition to lots of input from the top US competition pilots and recreational XC pilots. I have tried to make it a very easy to use yet sophisticated instrument.

Ease of use is a key feature in a S2F vario because a S2F vario requires much more interaction with the pilot than a simple climbing vario. This is the main reason the TFC had to be designed from the start for S2F: trying to adapt a simple climbing vario to S2F usually results in a very confusing interface. The TFC achieves ease of use by using a flexible text based display that allows variables to be displayed in whole words which makes it easier to understand. The keypad has very consistent functions so that the keys don't change their meaning in different screens. The result is that pilots who can't program their radios have no difficulty with the TFC.

In the air, the TFC audio makes looking at the display almost unnecessary. You adjust your next expected climb (speed ring) setting or head/tail wind setting with a few keystrokes. The TFC automates everything else. While gliding it gives you two tones, one to tell you to speed up and one to slow down, eliminating the need to look at the vario. Once you hit lift the Auto Switch feature automatically switches the audio to climb mode. Now you have the fastest responding digital vario on the market. Leave lift and the TFC switches back to glide mode audio. The Auto Switch feature is smart enough not to switch out of climb audio if you fall out of a thermal. For gliding in lift under cloud streets or on a ridge, the TFC can be manually switched into glide mode, or you can use the speed up/slow down indicator on the display.

Behind the scenes, the TFC takes care of the details. Every 20 seconds it recalculates the polar for your current altitude. Likewise with airspeed. This is very important because altitude has dramatic effects: At 2000, 4000 & 6000m your polar and airspeed change 13, 28 & 47%, respectively. Changing the wing loading will also recalculate the polar. A ballast input allows you to make temporary changes from your usual flight weight.

For the competition pilot, the TFC has a final glide calculator. This enables pilots to make goal without wasting time and helps prevent landouts. More than just an L/D calculator, the TFC takes your input on distance to goal and head/tail wind as well as your current climb rate and tells you how high you need to be to go on final glide. Climb rate is important: if you are climbing fast you will want spend time gaining extra altitude, which is later recovered by a faster glide speed. The glide speed is of course controlled by adjusting your next expected climb setting. If you are too high, increase the next expected climb setting, if you appear too low, decrease the setting. Using the final glide calculator can shave minutes off your time.

The TFC uses rechargeable nicad batteries that can be fast charged from AC mains or a cigarette lighter. Nicads are the best choice because of better low temperature performance than alkalines and far less fodder for the landfills: A nicad battery will take the place of 300 to 600 alkalines of similar capacity. The smart power management in the TFC allows quick charging (6 hours) and prevents damage from deep discharge.

The flexible display combined with upgradable software means that future improvements are easily added to existing units, protecting the pilot's investment.

John and Larry do not out glide me any more, but they can still make better decisions.

DETAILS OF THE ANALYSIS

To begin this analysis I needed a segment of air to fly the two gliders through that had a realistic profile of lift and sink. The air segment shown in Figure 6 is created from a flight during the 1993 World Championships. Since the recording rate was once per 15 seconds, the trace is the same as a recording of the 15 second averager of your vario. A barograph trace includes both the airmass sink or lift with the sinkrate of the glider added to it. Although this is related to what the air was doing, it includes in it the still air sink rate of the glider, so I created my test patch of air by subtracting out the sink rate of the glider. Since my barograph trace doesn't record how fast I was flying, you might ask how I know what the still air sink rate of the glider was. Since I was using a speed-to-fly vario I made the assumption that I was flying at the correct speed to fly, which I can calculate for each sink rate of each barograph point. I then plug this speed into the polar equation which gives me the still air sink rate of the glider which I can then subtract out to obtain the air mass movement.

Since I've calculated the speed I'm flying in each piece (barograph point) and I know I flew that speed for 15 seconds (the time between points), I can calculate how wide each piece is. Adding all these pieces up gives me the total length of the segment.

I do this for each 15 second long sample of the barograph trace to create a profile of the whole segment of air.

For each sample the procedure is as follows:

1) Calculate the vertical movement (Ws_indicated) by taking the difference in altitude of the next barograph point and the current point and dividing by 15 seconds (T_sample).

2) Calculate the speed (V_s2f) I should be flying in this vertical movement based upon the polar, the assumed speed ring setting (Cl) and Ws_indicated.

V_s2f = (-b - sqrt(b^2 - 8*a*(Cl - Ws_indicated))) / 4*a

Certain conditions can cause the above equation to yield meaningless or below stall air speeds. In that case I set the speed to stall speed.

3) Calculate the still air sink rate (Ws) of the glider using the speed polar:

Ws(V) = a*V^2 + b*V + c

4) The air mass sink rate is W_air = Ws_indicated - Ws(V_s2f).

5) The distance flown per sample is simply d_sample = V_s2f*T_sample.

Thus my segment of air consists of a whole bunch of little pieces of air which are going up and down at different rates and are doing so for different distances. Next I averaged the air over the segment to see whether or not on the whole the air is going up or down. Then I add a constant amount of lift or sink to each of the pieces to make my average air mass movement either rising, sinking, or net zero. In this analysis I create three air masses by "biasing" the segments so that there is an average -.25, 0 and +.25 m/s air mass movement over each of these segments. All three of these segments have the same shape, as shown in Figure 1 .

When flying The S2F pilot through the air segment, her optimum speed in each piece is calculated, from which I can calculate the altitude lost or gained and the length of time it takes the glider to traverse the piece. Adding each piece's altitude lost and its time gives me the total altitude lost and the total time. Achieved L/D comes from total distance and total altitude lost. Average speed comes from total distance and total time.

The constant speed pilot is now flown through the segment, only his speed is fixed at the average speed of The S2F pilot. His altitude lost and time to traverse each piece is calculated in the same manner, and then summed up. His total time will be the same as The S2F pilot's.

For each sample the procedure is as follows with the differences for Pilots A & B noted:

1) For The S2F pilot the speed flown in the sample is calculated based upon air mass sink (W_air), speed ring setting (Cl) and the polar coefficients (a, b & c).

V_sample = V_s2f = sqrt((c + W_air - Cl) / a)

The speed is set to stall speed if this equation produces meaningless or below stall speeds.

2) The still air sink rate (Ws) is calculated from the polar.

3) The altitude lost in the sample is

alt_sample = d_sample * ((W_air + Ws(V_sample)) / V_sample)

4) The time is simply T_sample = d_sample / V_sample.

Summing all alt_samples gives total altitude lost. Summing all t_samples gives total time to fly through the segment. For The constant speed pilot, the speed flown in every sample is:

V_sample = total distance / total time

The achieved L/D in the segment for each pilot is

L/D = total distance / total altitude lost