EVALUATING THE MANOEUVRING PERFORMANCE OF AN X-PLANE SUBMARINE
6. FREE RUNNING MODEL TESTS
Once the autopilot had been developed using a real time operating system the free running model tests could then
Warship 2011: Naval Submarines and UUVs, 29 – 30 June, 2011, Bath, UK
© 2011: The Royal Institution of Naval Architects be undertaken. This section presents details of these experiments conducted in both the Ocean Basin and at a deep water reservoir.
There were several aims to these free-running model experiments:
x to replicate the manoeuvres conducted using the equivalent cruciform model
x to explore high-speed manoeuvres
x to investigate the alternative control options offered by an X-plane arrangement
x to explore hydroplane jam responses and investigate recovery strategies
x to conduct manoeuvres suitable for System Identification, leading to improvements in the mathematical model predictions
The QinetiQ SRM is capable of all the above, but is chiefly used for exploring the extremes of the manoeuvring envelope [4]. The SRM was configured as a geosim of the model used in the constrained experiments, Figure 7. A standard set of instrumentation was fitted, comprising of a Ring Laser Gyro (RLG), Doppler Velocity Log (DVL) and pressure depth transducers, to undertake an extensive set of tests.
Figure 7: Profile view of SRM clad as an X-plane The experiments fall into two distinct parts: manoeuvres in the Ocean Basin and manoeuvres at the reservoir. In general, the Ocean Basin manoeuvres were limited to the slow and moderate speed runs and some limited depth changes. Some jam manoeuvres to rise were also conducted. The bulk of the programme was conducted at the reservoir where the available space allowed for the higher speed manoeuvres to be conducted as well as those which required larger depth changes.
In the Ocean Basin, the model is operated under driver control. The driver operated control desk functionality is limited, in part, by the bandwidth available for through- water communication. The driver has control of rudder and motor rpm, and through push-buttons can switch the autopilot on or off, or initiate certain manoeuvres such as turns, depth changes, zig-zag manoeuvres or hydroplane jams. The model is launched from a fixed cradle at one end of the tank and is driven up to speed, depth and heading and into the manoeuvring area. On completion of each manoeuvre, the model is brought to the surface,
captured by the divers and returned to the cradle for data off-load.
When operating at the reservoir there is no driver- communication system available. The model is effectively autonomous whereby all manoeuvres are pre- programmed, with events happening according to a fixed time sequence. The increased test area available at the reservoir allowed for several manoeuvres to be conducted in a single launch, provided the model is allowed time to recover onto speed, depth and heading between each evolution. For this reason, all runs were created in simulation first, the results of which also allow for planning of the approximate surfacing location.
By way of an example, turning circles form a standard set of manoeuvres which involve a set of parameters measurable from a turning circle manoeuvre. These include:
x Advance - defined as the distance travelled in the direction of the original heading between the helm-over order and the point of achieving a heading change of 90°.
x Transfer - defined as the distance travelled at right angles to the original track between the helm-over order and the point of achieving a heading change of 90°.
x Tactical diameter - defined as the distance travelled at right angles to the original track between the helm-over order and the point of achieving a heading change of 180°.
x Drift angle is the angle between the submarine’s heading and the direction of travel. In this case it has been calculated from the DVL data as drift angle = tan -1(v/u) once a steady state condition has been achieved.
Figure 8: Tactical diameter for a range speeds Figure 8 shows how the tactical diameter varies with rudder angle for a range of speeds tested. These turning circles were conducted using all four control surfaces as rudders, with additive depth control applied as required.
Because of the requirement for depth control, some of
Warship 2011: Naval Submarines and UUVs, 29 – 30 June, 2011, Bath, UK
© 2011: The Royal Institution of Naval Architects the 30° rudder turns did not quite achieve this angle. The
data show a consistent variation in the tactical diameter with rudder angle and are largely independent of speed.
There is a distinct “flattening off” at the higher rudder angles with no improvement in diameter at 30° rudder over 25° rudder, possibly as a result of the planes stalling.
As described earlier, the stability indices suggested that this X-plane design would be directionally unstable, so how did this manifest itself in the free running model tests? During the completion of a turn, where a pull-out manoeuvre is initiated, the yaw rate would persist; an example of a persistent yaw rate is given in Figure 9 which shows a pull-out at a speed equivalent to 8 knots.
Following a 10° rudder turn, the rudders are returned to midships. The yaw rate does decay, but settles on a non- zero value, i.e. the submarine keeps turning.
Figure 9: Example of yaw instability
Further experiments demonstrated that whilst in the vertical plane there was some transient instability, the design can be controlled by the planes without incurring excessive plane activity.
A series of tests included the application of a single hydroplane jam following a steady period of straight and level running. All other control surfaces remained under autopilot authority, and the initial response was to “do nothing”, i.e. allow the autopilot to simply carry on with the current ordered depth and heading.
An example of an 8 knot jam to rise is shown in Figure 11. Generally, for modest jam angles of say 10° and 20°, any pitch, depth and yaw excursions were minimal.
However, for the higher 30° jam to rise on the upper port plane, shown in Figure 10, the excursions were more considerable, and yaw became uncontrolled. The initial response of the course keeping and depth keeping controllers is to control yaw and pitch equally; however, both failed in this scenario. When the heading error reached 10°, the autopilo t switched to the course- changing controller which had no integral action. As such the demands of the heading control then become swamped by the depth control so the submarine is no longer controlled in yaw. As a result the control of depth and pitch are regained at the expense of increasing the yaw rate.
Figure 10: Single plane jam at 8 knots
As mentioned earlier a simulation framework was created which allowed all of the manoeuvres to be replicated with a single command. In order to simulate the free-running model as best as possible, there are several initialisation tasks required.
x The simulated rpm must provide the correct speed
x The acceleration, deceleration and braking characteristics must agree.
x The balance angles and compressibility must be established to correctly account for loss of buoyancy during depth changes
All the standard and jam manoeuvres have been replicated in simulation but only a single representative example is given here. Figure 11 shows the comparison between simulation and experiment of a single plane jam to dive at a speed equivalent to 18 knots.
The simulations of the excursions following a single hydroplane jam are reasonably well predicted. For the higher plane jams in Figure 12, the simulations are a little optimistic. In this example, for the first 5 seconds of the jam the first few degrees of the pitch and yaw excursions are well modelled. From 5 seconds onwards, the model continued its excursions rapidly, whereas the simulation starts to hold a steady state. This could possibly be due to a lack of modelling of the stall characteristics of the control surfaces, although this would apply equally to the jammed surface as well as to the recovery surfaces.
However, the characteristics are likely to be different since some hydroplanes will be in the wake of the
Warship 2011: Naval Submarines and UUVs, 29 – 30 June, 2011, Bath, UK
© 2011: The Royal Institution of Naval Architects submarine and some will not. The mathematical model does not currently include this detail.
Figure 11: Simulation of single plane jam with turning In general, single hydroplane jams at moderate angles were comfortably dealt with by the autopilot without any further action, with depth and heading successfully maintained. However, single hydroplane jams at the maximum deflection were not successfully controlled by the “do nothing” strategy. An alternative strategy of slowing down and allowing heading changes meant that depth and pitch were better maintained. However, depth was not always fully recovered (i.e. zero depth rate) so further options should be considered.
Although the simulations show good agreement in many areas, there are a number of points for further investigation. Depth and pitch response prediction in a turn have been improved for controlled turns, but still require investigation in free turns and hydroplane jam scenarios. The poor roll predictions during turns also require investigation.
7. PRELIMINARY SAFE OPERATING