Long Explanation

The Problem

As soaring pilots we are trying to find either the least bad (sinking) air or the best (rising) air. The unaided human finds this difficult without the help of an instrument in the glider known as a variometer.

The energy state of a glider at any moment is the sum of the potential energy (energy due to height in Earth’s gravity field, mgh, where m is mass of glider, g is acceleration due to gravity and h is the height) and the kinetic energy (energy due to glider forward speed, ½ mv^2 where v is the speed of the glider – actually the True Air Speed) and if the pilot changes the glider pitch attitude from steady speed flight these may be interchanged but at any moment the total energy is unchanged.

This results in either extra sink or less sink or even a climb being indicated on the uncompensated (connect to Static only) variometer even though the airmass being flown in has not changed its vertical velocity.

An uncompensated (Static, non total energy) variometer will show only the rate of change of the potential energy and this may be quite large when, for example pulling up into a thermal or leaving one to accelerate to cruising speed, completely masking any smaller changes in the vertical motion of the airmass being flown in while the glider speed is changing.

More than 70 years ago this problem was avoided by measuring the Total (kinetic + potential) Energy of the glider, which requires in addition a signal which is sensitive to the airspeed of the glider (kinetic energy) as well as the rate of change in altitude (rate of climb/descent or potential energy change)

The rate of change of airspeed multiplied by the airspeed is the rate of change of kinetic energy. This is the same magnitude as the rate of change of potential energy but opposite in sign so the two signals cancel.

In fact it is the change in angle to the previous equilibrium angle at constant speed induced by the pilot that determines the rate of change in airspeed. Acceleration due to gravity multiplied by the trigonometric Sine of the angle change equals the rate of change in airspeed. In a vertical climb induced by the pilot the speed will change at minus one G acceleration plus a little bit due to glider drag. Similarly in a vertical dive the glider accelerates at plus one G acceleration minus a little bit due to aerodynamic drag. In between, the rate of change depends on the Sine of the angle.

Seventy years ago there was no good way to measure that angle change directly so it was inferred by measuring the rate of change of airspeed instead.

At the time the total energy sensor connected to the variometer was typically a venturi (more speed, more suction) with just the right throat to intake and exit area, instead of a connection to the glider static ports. As a pilot pulls up the air pressure becomes lower but the glider slows down, so there is less suction in the venturi and this counteracts the reduction in air pressure so the variometer reading is essentially unchanged. This worked quite well on the sailplanes of the time which rarely flew much faster than 60 knots between thermals. Later various simpler to manufacture and sometimes lower drag devices such as the Irving probe were introduced but their function was the same as that of a simple venturi.

If airmass motion consisted only of vertical motion with no horizontal components this system would be completely satisfactory for sailplanes which flew at any speed, including the up to 140 knot TAS (True Air Speed) which can happen with a good modern glider at high altitude on an excellent day.

As glider speeds became higher with better aerodynamic design and higher wing loadings, it was noticed that Total Energy variometer performance deteriorated, with many large false indications occurring. These are caused by air motion changes with a horizontal component. A horizontal gradient of only one knot per 50 meters while flying at 100 knots TAS (maybe only 80 knots indicated if you are up high around 10,000 feet AMSL) will cause a 5 knot indication on the Total Energy variometer even when no changes in vertical motion are present.

This false indication is the rate of change of airspeed multiplied by the airspeed (both TAS), exactly as for the kinetic energy change measurement. If you fly twice as fast through a given horizontal gradient, the airspeed is twice as large and the rate of change of airspeed through the same air is twice as large so the effect is four times as large.

In fact a change from 50 to 51 knots is small – only 2%, but it is multiplied by the rate of change of a half of one knot per second. This causes a lift indication of about 1.25 knots, not so bad. Fly twice as fast (100 knots) through the same air and the rate of change is one knot per second even though the speed change itself is only one percent (100 to 101 knots). This results in a lift indication of 5 knots which is highly misleading.

It is impossible to filter this as it is intrinsic to the way a TE vario works, as we have seen above. Make the vario slower and as well as reducing the effects of the horizontal unsteadiness you lose information on the vertical changes of interest. The result is that the variometer indications show both vertical and horizontal airmass changes while we want only the vertical ones. The two are completely mixed up and are of similar size and time duration so the pilot uses other inaccurate cues such as the vertical g load changes (seat of pants) to determine whether the variometer indications are from vertical or horizontal airmass events.

A tiring, high mental workload is the result with a high error rate and distraction from other tasks. A horizontal gust which goes on for 5 or more seconds may induce the pilot to turn, wasting 30 seconds to a minute as there was no thermal there. Doing this several times on a flight will result in significant loss of average speed.

The Solution

We have seen that the total energy compensation signal is given by rate of change of airspeed multiplied by airspeed with the rate of change of airspeed factor being the problem, caused by measuring the airspeed directly.

In theory we could measure the angle change with a high accuracy attitude indicator but unless driven by a set of ring laser or fiber optic gyros (read very expensive and power hungry), attitude indicators will easily keep you right side up in IMC but are not accurate enough for our purposes here. In addition they may use rate of change of airspeed to stabilise the pitch indication making them completely useless here.

Fortunately, with modern technology, it is now possible at realistic cost and power consumption to directly measure the change in angle to the horizon of the glider trajectory. Note that this RATE of change DOES NOT depend on airspeed measurement directly so is immune to the effects of the horizontal unsteadiness in the atmosphere.

By using two GNSS (Global Navigation Satellite System) receivers (or one which is essentially two in one package) of the right type we can directly measure the pitch and heading to better than 0.1 degrees in a completely stable manner, directly oriented to the Earth horizontal plane. We can use accelerometers in the aircraft oriented fore and aft and up and down to directly measure a combination of glide angle and angle of attack, no matter the attitude of the glider. There are offsets due to the mounting angle between the GNSS antennas, the accelerometers and the glider zero effective angle of attack, which are removed by the Dynamis algorithms and the air data system.

Correct operation during turns requires knowledge of the bank angle which is determined by TAS, rate of change of heading (turn rate) and G loading. There is also the effect of sideslip while banked which will show up in pitch. A third accelerometer oriented across the wingspan compensates for this.

The uncompensated vertical motion is determined by the GNSS vertical motion output, a very accurate, stable, fast and low noise source and the Sine of the angle change multiplied by TAS is the TE compensation signal. The TAS varies slightly in horizontal gusts but this is of no consequence as, worst case, the total energy error is 1 to 2% and mostly a lot less, which is undetectable.

The two dimensional velocity from the GNSS gives a very accurate direction and speed over ground signal, the heading from the system and the TAS give the glider speed and direction through the air so the 2 dimensional wind triangle is calculated many times a second and the average is displayed over any time period the pilot sets, whether circling or flying straight.

The Dynamis variometer is a true Total Energy variometer, not an airmass system, which works both in straight cruising flight and during turns and which behaves exactly like the traditional pressure based Total Energy variometers EXCEPT that it is immune to the effects of horizontal gusts, indicating only changes in vertical air motion. It accurately measures various physical variables and straightforwardly process the measurements without exotic mathematical algorithms or assumptions about likely glider or airmass motion. Mathematical trickery is no substitute for proper, accurate measurement. Only one variometer pointer is required as the indications are solid and reliable.

Removal of the pilot mental filtering workload and misleading indications of thermals are huge benefits. The variometer indication is MUCH steadier yet very fast in response and responds only to changes in vertical motion of the air. The Dynamis variometer information is used in the Relative Netto and speed command calculations making both indications FAR more steady and useful.

The Dynamis system was flying in 2016 with final correction of the internal calculation algorithms in late 2018. A batch was constructed and sold in 2019 with generally good results after some in service RF connector issues were identified and resolved. This batch used a straight GPS only receiver which meant that only 7 to 12 satellites were visible at any one time which was fine in cruising flight but could result in loss of RTK during circling at steep bank angles depending on the satellite configuration at the time. The system was set to auto revert to pressure variometer in this case.

In mid 2020 a new GNSS receiver became available. This uses all satellite constellations concurrently (GPS – USA, Glonass – Russia, Galileo – Europe and Beidou – China, as well as QZSS – Japan and IRNSS -India). The second last is only available in the area close to Japan and the same longitudes in the Southern Hemisphere though over a wider area and the last is over the Indian Ocean area where the satellites are in figure 8 Geosynchronous but not Geostationary orbits.

No fewer than 30 satellites and up to 40+ are visible in North America, Southern Africa and Europe at all times and 50 to 60 are visible in Australia/New Zealand. As the RTK system only requires 8 satellites to maintain RTK fix there are no signal dropouts even at steep bank and pitch angles as proven by extensive test flying. The auto revert to pressure mode has not been required.

Compared to the legacy units, the new GNSS greatly simplifies installation. The antenna ground planes are only 100mm diameter instead of 200mm. Instead of one receiver with co-axial cable to the antennas, there are two receivers connected by a simple 3 wire shielded cable with an outside diameter of 3mm so only a 3.2mm (1/8”) hole in the glider skin is required. It is possible to do a temporary install by taping the 3 wire cable to the outside of the glider and feeding it to the cockpit through an extractor vent but you will likely do only one flight before permanently installing it.

The new GNSS is more accurate than the old GPS units so the required baseline distance between the two antennas is only 2 meters. In a small fuselage Ventus the aft antenna can be mounted 2.2 meters behind the front antenna and still feed the connecting cable into the oxygen bottle compartment.

There is still a small aerodynamic fairing on top of the fuselage. This should be considered as a Total Energy probe. The Dynamis fairing has approximately one seventh of the drag of the traditional ¼” or 6mm diameter Irving type probe (Hoerner – Fluid Dynamis Drag). Total drag can be reduced by using our MiniTE probe of 3mm diameter which has approximately one quarter the drag of the legacy probe, still resulting in a useful overall drag reduction even with the Dynamis fairing.

Dynamis changes the internal algorithm depending on whether it is in straight or circling flight and this is now done automatically. The pilot still has a cruise/climb switch so the variometer indications can always be what the pilot desires at the time. It is also possible to use a flap switch.

The new receiver and variometer system have gone through many firmware updates and are now very stable and very reliable. Along with extensive test flying, a handful of software bugs in the Dynamis variometer system were identified and removed over the last 3 years, the digital display now has a new font and is tidier and we believe it is time for commercial release of the new Dynamis.