Fig. 7. Gliding angle with respect to the movable mass displacement, with
fixed net buoyancy of -20 g.
2 3 4 5 6 7 8
12
14
16
18
20
22
24
V (cm/s)
r
p
(mm)
Experiment data
Model prediction
Fig. 8. Gliding speed with respect to the movable mass displacement, with
fixed net buoyancy of -20 g.
Furthermore, we use the collected data to fine-tune the value
of zCG.
Fig. 7 and Fig. 8 show the comparison between model
predictions and experiment results when we vary the movable
mass positions while holding the net buoyancy fixed, and
Fig. 9 shows results when the net buoyancy is changing while
the movable mass location is fixed. From the comparison
results, we can see that the velocity and gliding angle calculated from the model match the experimental data reasonably
well. In particular, the model has predicted well the trends of
how glide speed and angle vary with the center of the gravity
and the net buoyancy. We also want to point out that there
are some non-ignorable errors in the measurement. When
the glider starts glide from rest, it is accelerating rather than
steadily gliding. We have already tried to remove the accelerating section from the data; however, it is difficult to do
precisely, especially considering the relatively shallowness of
−26 −24 −22 −20 −18 −16 −14
12
14
16
18
20
22
24
26
V (cm/s)
m
0 (g)
Experiment data
Model prediction
Fig. 9. Gliding speed with respect to the net buoyancy, with fixed movable
mass displacement of 0.5 cm.
4s
-30.22e
5s
-23.38e
6s
8.79e
7s
30.64e
8s
33.94e
9s
24.32e
Fig. 10. Illustration of transient gliding motion with snap shots.
the test tank. This effect will be reduced with deeper gliding;
however, conducting precise measurement in a deep water
body itself presents many challenges. Also the environmental
disturbances such as currents will influence the experiment
results. So with these uncertainties, we consider the match
between our experimental results and the model predictions
satisfactory.
B. Dynamic Gliding Model Validation
For the dynamic gliding model validation, experiments
are performed in the same way as those for static model
validation, but this time we take videos of the glider during
its transition from diving to upward gliding. Then we analyze
the video frame by frame to obtain the time sequence of
the pitch angle as shown in Fig. 10. On the mathematical
model side, simulation is carried out with the parameters
set according to the experiments. The two adjustable inputs,
net buoyancy m0 and movable mass displacement rp, start
at 20g and 0.5 cm respectively, and keep that value until 1
second. Then m0 decreases with constant pumping rate to
−20g in 9 seconds and then remain that net buoyancy, while
4909
0 2 4 6 8 10 12
−40
−30
−20
−10
0
10
20
30
40
θ (°)
t (s)
Model prediction
Experiment data
Fig. 11. Pitch angle during transients of the glider from downward glide
to upward glide.
r
p changes with constant translational speed to −0.3 cm in
0.5 seconds and then stay with that position. The simulation
result is presented in Fig. 11 together with results from two
experimental trials. From this figure, we can see clearly that
the model predicts well the transient dynamics of the glider,
including both the overshoot and oscillation behaviors.
Fig. 7. Gliding angle with respect to the movable mass displacement, withfixed net buoyancy of -20 g.2 3 4 5 6 7 812141618202224V (cm/s)rp(mm)Experiment dataModel predictionFig. 8. Gliding speed with respect to the movable mass displacement, withfixed net buoyancy of -20 g.Furthermore, we use the collected data to fine-tune the valueof zCG.Fig. 7 and Fig. 8 show the comparison between modelpredictions and experiment results when we vary the movablemass positions while holding the net buoyancy fixed, andFig. 9 shows results when the net buoyancy is changing whilethe movable mass location is fixed. From the comparisonresults, we can see that the velocity and gliding angle calculated from the model match the experimental data reasonablywell. In particular, the model has predicted well the trends ofhow glide speed and angle vary with the center of the gravityand the net buoyancy. We also want to point out that thereare some non-ignorable errors in the measurement. Whenthe glider starts glide from rest, it is accelerating rather thansteadily gliding. We have already tried to remove the accelerating section from the data; however, it is difficult to doprecisely, especially considering the relatively shallowness of−26 −24 −22 −20 −18 −16 −141214161820222426V (cm/s)m0 (g)Experiment dataModel predictionFig. 9. Gliding speed with respect to the net buoyancy, with fixed movablemass displacement of 0.5 cm.4s-30.22e5s-23.38e6s8.79e7s30.64e8s33.94e9s24.32eFig. 10. Illustration of transient gliding motion with snap shots.the test tank. This effect will be reduced with deeper gliding;however, conducting precise measurement in a deep waterbody itself presents many challenges. Also the environmentaldisturbances such as currents will influence the experimentresults. So with these uncertainties, we consider the matchbetween our experimental results and the model predictionssatisfactory.B. Dynamic Gliding Model ValidationFor the dynamic gliding model validation, experimentsare performed in the same way as those for static modelvalidation, but this time we take videos of the glider duringits transition from diving to upward gliding. Then we analyzethe video frame by frame to obtain the time sequence ofthe pitch angle as shown in Fig. 10. On the mathematicalmodel side, simulation is carried out with the parametersset according to the experiments. The two adjustable inputs,net buoyancy m0 and movable mass displacement rp, startat 20g and 0.5 cm respectively, and keep that value until 1second. Then m0 decreases with constant pumping rate to−20g in 9 seconds and then remain that net buoyancy, while49090 2 4 6 8 10 12−40−30−20−10010203040θ (°)t (s)Model predictionExperiment dataFig. 11. Pitch angle during transients of the glider from downward glideto upward glide.r
p changes with constant translational speed to −0.3 cm in
0.5 seconds and then stay with that position. The simulation
result is presented in Fig. 11 together with results from two
experimental trials. From this figure, we can see clearly that
the model predicts well the transient dynamics of the glider,
including both the overshoot and oscillation behaviors.
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