[3] aiaa_improvedsurfacemarkerbuoyforscubadivers

American Institute of Aeronautics and Astronautics

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Improved Surface Marker Buoy for Scuba Divers

Maung, M.T.*, Sakumoto, K.N†. Sato, C.I.‡, and Uchimura, B.M.§ University of Southern California, Los Angeles, California, 98009, USA

An off-the-shelf surface marker buoy (SMB) for scuba divers was redesigned with capability to stabilize autonomously at the surface, not submerge more than 40% at the surface, minimize its vertical ascent velocity, and inflate using an inflation mechanism integrated into the SMB. Three variants were analyzed for form and function: passive nozzle control stabilization, drag chute stabilization, and weight apparatus stabilization. Using analysis from numerical modeling, fabrication, and test and evaluation, the weight apparatus variant was the variant that best sufficed all design criteria. The weight apparatus consisted of a weight suspended from the base of the SMB that emulated the tension force current SMBs use for surface stability. For the 1.1 m (3 ft 8 in) height SMB tested and the 40% SMB submersion criterion, the maximum allowable mass of weight apparatus was 0.820 kg, but 0.450 kg was required for surface stability. Fabrication dictated a 0.526 kg mass of weight. Numerical and experimental models confirmed the tested SMB returns to 0±10° within 4 s when deflected up to 60° from the vertical. A terminal velocity of 4.09±0.01 m/s was achieved resulting in a numerically calculated 7.56±0.02 s SMB ascent time from a 35 m depth, compared to 4.64±0.01 m/s and 8.59±0.02 s respectively for the SMB without the weight apparatus. An off-the-shelf road bicycle tire CO2 refill canister and nozzle was integrated into the final design, that used the weight apparatus prototype, to meet the self-contained inflation requirement. The proposed final design shares the same governing equations as the prototype, and therefore physical behavior is expected to be shared. The modular nature of the final design allows it to be used in place of current SMBs.

Nomenclature A = cross-sectional area of SMB CD = drag coefficient of SMB FB = buoyancy force of SMB FD = drag force of SMB Fg = weight force of SMB FTHRUST = thrust force of SMB M = restoring moment of the SMB t = time tss = steady state time U = velocity of SMB during ascent Uterminal = terminal velocity of the SMB during ascent V = volume of SMB submerged in fluid θ = angle pertuabation of SMB ρ = density of fluid surrounding the SMB

I. Introduction surface marker buoy (SMB) is a signaling device used by scuba divers that, when inflated and released at

depth by the diver, ascends to the surface to signal the location of the submerged divers to bystanders at the surface. Figure 1 depicts a typical SMB unit. * Aerospace and Mechanical Engineering, [email protected], AIAA Member † Aerospace and Mechanical Engineering, [email protected], AIAA Member ‡ Aerospace and Mechanical Engineering, [email protected], AIAA Member § Aerospace and Mechanical Engineering, [email protected], AIAA Member

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Divers use SMBs by attaching the SMB to a line wound around a

reel, inflating the SMB with air from the diver’s air regulator or medium-pressure hose, releasing the SMB to allow its ascent, and finally applying tension to the reel line when the SMB surfaces to stabilize the device in a vertical position. The SMB usage process can be characterized into two segments: ascent to surface and stability at surface.

The SMB ascent to the surface can be characterized by considering the force balance of the SMB during this

phase. A force diagram of the SMB was considered to identify the main forces acting on the SMB. From Figure 2, there are three forces acting on the SMB: the weight W, the drag force FD and the buoyant force

FB. The weight of the SMB is given by

Fg = mg (1)

where m is the mass of the SMB. Similarly, the buoyant force equation is given by

FB = ρVg (2)

where 𝜌 is the density of the submerged liquid and V is the volume of submerged portion of the SMB. The volume of the SMB increases as the SMB ascends due to Boyle’s Law because the pressure at depth is much higher than the pressure at surface so the volume of the SMB changes accordingly shown by (3).

P1V1 = P2V2 (3)

Since the volume of the SMB increases as it ascends, a passive pressure relief valve is incorporated into the

SMB in order to maintain a constant volume throughout the ascent. The drag force that acts on the SMB is given by

FD = 0.5ρU2CDA (4)

where U is the velocity, CD is the coefficient of drag and A is the cross-sectional area. There are a few assumptions made in the numerical model. The first assumption is that the SMB’s volume stays

constant. Once the SMB is inflated to its maximum volume, it cannot expand any further without tearing. The second assumption is the drag coefficient of the SMB is a cube and its corresponding drag coefficient from theory is given as CD = 1.05. Moreover, the temperature of the surroundings is assumed to be constant. This is a fair assumption since the temperature gradient of the SMB at a depth of 5 m to 35 m is constant.2

Similar to the temperature, the density gradient as a function of depth is negligible for the case of 5 m to 35 m.2

Even the largest differential of density has a differential of less than 0.5% so it is appropriate to assume density to be constant.

The surface stability of the SMB can be characterized by the moment balance of the SMB during this phase. The

model in Figure 3 accounts for an external perturbation force, FEXT, and an initial perturbation angle, θ, from which the SMB attempts to recover. The moment, M, is the restoring moment of the SMB. The buoyancy force, FB,

Figure 1. Typical consumer-grade SMB. A typical SMB height is 3 ft to 6 ft with a diameter less than 0.5 ft.4

Figure 2. Free body diagram of the SMB with the filled black circle representing the passive relieve valve.


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location is simplified by assuming the SMB body is a 1D rod because FB x-location does not significantly impact the perpendicular force. The buoyancy of the weight apparatus is ignored because the volume of the weight apparatus is far less than the volume of the SMB body.

The pressure-induced forces on either side of the 2D version of the SMB, FH20_1 and FH20_2, have magnitudes

driven by the area on either side of the SMB that is submerged. The area, A, is approximated by

𝐴 ≈ 𝑙!"#$%&'%( !"#$%&' ∗ 𝑑!"# !"#$ (5)

where l is the length of the submerged section of the SMB body and d is the diameter of the SMB body.

To determine the restoring moment of the SMB, MSMB, a moment balance is formulated using the 1D rod approximation, buoyancy of weight apparatus approximation, and area calculation formulation:

𝑀!"# = 𝑟!"#𝐹!"# + 𝑟!𝐹!!"_! + 𝑟!𝐹!!"_! + 𝑟!𝐹!𝑠𝑖𝑛𝜃 + 𝑟!𝐹!𝑠𝑖𝑛𝜃 (6)

The tension and buoyancy forces dominate the angular acceleration of the SMB, however, the drag force can

also be considered as a damper force.

𝐹! = 0.5𝜌!!"(𝜔𝑟!2)!𝐶!𝐴!!"_! (7)

where the velocity is equal to the angular velocity scaled by the average length of the submerged SMB. The drag force is what returns the SMB to a stable state from an oscillating state. The SMB surface stability can be characterized as a second-order system.

𝐽!𝜃 = 𝐶1!"#$ !"#"$%&𝜃 + 𝐶2!"!#$% !"#"$%&𝜃 (8)

where C1 and C2 are the coefficients that characterize the drag and moment balance forces of the SMB and J0 is a generalized moment of inertia.

Characterizing both ascent to surface and stability at surface shows that the mass or drag of the SMB must be

increased to reduce speed, thus increase stability. Additionally, the tension force, FT, must exist to ensure the SMB submerges resulting in a drag damper force to ensure surface stability.

(i)

(ii) (iii)

Figure 3. Forces contributing to the SMB’s surface stability and defined coordinate system in the non-perturbed (i) and perturbed (ii) positions. A detailed view of the (ii) submerged section is shown by (iii). (ii) and (iii) share coordinate systems.


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II. Design Problem and Requirements This SMB usage process also has several tedious or complex steps that pose problems particularly to beginner

scuba divers. These problems include: reel jamming from mechanical failures from high cycle, uncontrollable ascent defined by a greater than 5 m/s terminal ascent velocity, and complex inflation of SMB defined by the requirement for the diver to remove the mouthpiece air regulator to inflate the SMB. To address these problems, four design requirements were proposed for the improved SMB:

1. Stabilize autonomously at the surface 2. Submerge no more than 40% of total height at the surface 3. Minimize vertical ascent velocity 4. Inflate without pressurized air from the diver’s air tank

To design an improved SMB that met the four design criteria, a design process was developed to structure the

decision to begin designing and building a prototype.

III. Design Process An iterative design process was formalized to guide the design process to choose a preferred variant for the final

improved SMB design. The design process is outlined in Figure 4.

The prototype phase consisted of developing a MATLAB model of ascent and stability at the surface of the SMB, fabricating a functional prototype, and testing and evaluating the functional prototype. At any step of this phase, a no-go decision could have been made based on the results of each step showing limitations of the variant. If the variant performed adequately through all three prototype phase steps, the decision to design a final product was made. The next section outlines the three variants that were investigated as part of the iterative design process.

IV. Design Iterations Three variants were developed using the design process: a passive nozzle control system, drag chute, and weight

apparatus. Figure 5 shows a diagram of all three variants.

Figure 4. Flowchart of SMB design process shows steps 1-3 (prototype phase), decision gate, and step 4 (final product design).

(i)

(ii)

(iii)

Figure 5. Conceptual drawing of the each SMB variant: passive nozzle control system, drag chute, and weight apparatus variants (left to right).


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The passive nozzle control system variant consisted of three passively controlled nozzles positioned on opposing sides of the SMB mid-section. An excess mass flow nozzle would be placed at the base of the SMB. Each nozzle had a valve that released air to keep the vertical trajectory. Next, the drag chute variant consisted of a drag chute of a specified area and height positioned at the base of the SMB. The chute would create drag during ascent and shift the CG of the SMB lower, and likewise create a force replicating the required tension force, for surface stability. Lastly, the weight apparatus variant adds mass to the SMB to reduce its terminal velocity and directly replicates the tension force required for surface stability.

A. Passive Nozzle Control System The nozzle thrust force performance calculated using a

numerical model limited the viability of the passive nozzle control system. A physical model of the forces acting on the SMB is shown in Figure 6. In addition to the forces described in (1), (2), and (3), the thrust force, FTHRUST, shapes the numerical model of the nozzle control system.

This thrust force was proposed to be similar to a rocket-like mechanism that propelled the SMB upwards as described by the Reynolds’s Transport Theorem for momentum as shown in (8).3

The first integral in (8) is the rate of change of momentum and is

zero in this case since it represents rate of increase of momentum in the control volume in the non-inertial frame. The second integral represents the thrust provided by the air inside the SMB so (8) can be represented by

𝐹!"#$%! = 𝜌!"#𝑈!"##$%! 𝐴!"##$% (9)

Figure 7 illustrates the negligibility of the force from one thruster, FTHRUST, compared to the other forces, FB and

FD, acting on the system. The negligibility of FTHRUST

compared to the other acting forces means the SMB cannot be adequately controlled using thrusters. Additionally, the complex mechanics of the proposed system would result in a SMB sensitive to high-pressure external environments including that at 35 m depth.

B. Drag Chute Fabrication constraints, not numerical modeling results, limited the viability of the drag chute variant. Two cross-sectional area shapes were tested, a square and a hexagon, but both variants experience structural issues outlined in Figure 8.

time [s]

Figure 6. Model of all forces acting on passive nozzle control system variant derived from Figure 2 with addition of FTHRUST from nozzles.

Figure 7. FB and FD plotted against FTHRUST for 1.1m (3 ft 8 in) height SMB ascending to the surface from a depth of 35 m. FB and FD >> 1 N. FTHRUST << 1 N.

𝐹! −𝑊 −𝑚�̈� =𝛿𝛿𝑡∫ 𝜌𝑢𝑑𝑉 + ∫ 𝜌𝑢(𝑢 ∙ 𝑑𝐴) (8)

FD FB FTHRUST

t

force


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The adhesive connecting the SMB body to frame separated during multiple cycles due to the FD >> 1 N

experience by the chute A = 0.2 m2 profile area. The joints, from the same forces, also inappropriately collapsed during the ascent and at the surface. Optimization of the design for consumer required that the device collapse into a portable package. Additionally, only non-destructive fabrication techniques could be used to adhere the chute to the SMB, and creating the SMB and chute in one-piece would intensify the fabrication process.

C. Weight Apparatus 1. Numerical Model The numerical model for the weight attachment apparatus is very similar to that described in Figure 2. The design for the weight apparatus that accomplishes stability during ascent and at surface is greatly desired. To accomplish this, the numerical model finds the appropriate dimensions of the weight apparatus that accomplishes the design requirements. The model of the weight apparatus and its corresponding forces are shown in Figure 9. The force balance of the weight apparatus model is given by

In (10) above, the only sizable factor is the mass of the weight apparatus so the sizing of the weight apparatus is determined by the performance of the SMB. The first performance factor that is considered is the percent submerged of the SMB with respect to the mass of the weight, which is shown in Figure 10. Thus, any SMB with a mass of the weight apparatus below the 0.820 kg limit will ensure the SMB meets the design requirement.

Figure 8. Failure points of the drag chute variant. (1) Adhesive connecting SMB body to drag chute and (2) Joints connecting rods for drag chute frame.

Figure 9. Model of the weight apparatus with the forces acting on the system.

∑𝐹 = 𝜌!!"𝑉!"#𝑔 −12𝜌𝑈!𝐶!𝐴!"# − !𝑚!"#$!! !""!#!$%& + 𝑚!"#!𝑔

(10)

Figure 10. Percent of SMB submerged relationship with the mass of the weight apparatus. The 40% submerged height requirement limits the mass of the weight apparatus to 0.820 kg.


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There are two stages that describe the ascent of the SMB. The first stage is the initial deployment of the SMB and at this stage, the acceleration of the SMB will be positive because the SMB is not at its terminal velocity. The second stage is characterized by the acceleration of the SMB being zero once the SMB reaches terminal velocity. Figure 11 and (10) best describe this. (10) shows that the force balance is not zero immediately. This is because the drag term is zero when the SMB is not at its final velocity yet. Solving (10) for the terminal velocity yield

𝑈!"#$%&'( =2(𝐹! − 𝐹!)𝜌!!"𝐴𝐶!

(11)

In Figure 11, the forces of the SMB are the same after a short period, which indicates that the SMB has reached

terminal velocity. From the numerical model results in Figure 12, the SMB reaches terminal velocity at t << 1 s, so

the SMB maintains constant velocity for most of its ascent, which is desirable for minimizing tumbling and entanglement. The numerical model results shown in Figure 11 uses a weight apparatus of 0.526 kg. This mass is chosen from the readily available masses for the weight apparatus that were available, and the mass of 0.526 kg fulfills the requirement of the maximum allowable mass of 0.820 kg. For this given mass compared to the SMB without any weight apparatus, the velocity of the SMB as a function of time is derived from the numerical model as shown in Figure 12.

Figure 12 shows that the SMB reaches Uterminal at less than 0.1 s, which confirms that U is constant for most of the ascent. The difference is that the SMB with a weight apparatus of 0.526 kg has Uterminal = 4.09 ± 0.01 m/s while a SMB without a weight apparatus has Uterminal = 4.64 ± 0.01 m/s For the same weight attachments, the ascent time of the SMB from a depth of 35 m is compared in Figure 14. Thus, the difference in Uterminal is 11.8%, which was

determined to be minimal. From Figure 13, from a depth of 35m, the SMB

reaches surface in 7.56 ± 0.02 m/s without any weight apparatus. With a weight apparatus of 0.526 kg, the SMB reaches surface in 8.59 ± 0.02 m/s seconds. The SMB takes 12% more time to rise to surface with the weight apparatus, which achieves the design requirement of slowing down the vertical ascent velocity, U. The numerical simulation also shows Uterminal against the mass of the weight apparatus as shown by Figure 14. From Figure 14, it is seen that the difference in Uterminal for a weight attachment of 0.500 kg to 0.820 kg is 0.38±0.02 m/s. This does indicate a significant Uterminal

Figure 13. Ascent model of the SMB with different weight apparatus masses for a depth of 35 m.

Figure 12. Velocity of the SMB as a function of time for a SMB without a weight apparatus and a SMB with a weight apparatus with mass 0.526 kg.

Figure 11. The forces acting on the SMB as a function of time with emphasis at the point where the SMB reaches terminal velocity.

t

t t

force

FD FB

U


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difference between the two weight apparatuses, but it is already demonstrated that the SMB ascends at a constant velocity for most of its ascent so the particular terminal velocity value should not be of importance, which is why the mass attachment should be sized according to surface stability requirements.

From (5), (6), and (7) a MATLAB model using time-steps to model the dynamic second-order response was created and produced the following response in Figure 6 for a θ = +60° deflection. (7) requires that the SMB is submerged, but if the SMB is not submerged, the SMB will never return to a stable steady state. Therefore, considering Figure 16 and the mass limitation, a mass of 0.526 kg was used in the numerical calculation

Figure 15 shows that the SMB

converges to a stable position, defined as 0±10°, in 2 s. The steady state time, tss, is below 10 s, which was defined as the acceptable time to stability. Additional numerical simulation tests were conducted at θ = ±10°, ±50°, and ±89° to analyze a full spectrum of deflections. The sign of the deflection was irrelevant to stable steady state time.

The tss increases as θ increases. However, at maximum θ = 89° defined as the maximum of the model’s validity, tss < 10 s, which is

still the acceptable time to stability. Thus, the model shows the SMB has an adequate surface stability response meeting the design requirement. The numerical models implied a working design, and therefore a prototype was fabricated for functional testing.

2. Fabrication The MATLAB models helped to verify that a

prototype with a weight apparatus attached to it at the bottom would work to fulfill the design requirements. To keep costs low but still have a functioning prototype, a simple test rig was made out of the SMB, a 0.500 kg mass, a rod with an “O” loop, and a nut totaling to a mass of 0.526 kg. The “O” loop locked into the snap-hook at the base of the SMB. This test rig is shown in Figure 16. The mass of 0.526 kg was chosen based on available materials and the MATLAB models. This test rig was chosen for its simplicity and low cost because the materials were readily available.

Figure 15. Angular position time response of SMB when deflection θ = +60° respecting corresponding coordinate system.

Table 1. Time to Steady State for a Given SMB Deflection Angle

θ (°) tss (s) 20 1.3 50 1.8 89 2.2

Figure 16. A picture of the weight apparatus, consisting of a rod, a 0.500 kg weight, and a nut to secure the weight.

Figure 14. Terminal velocity versus weight apparatus mass.

Uterm

inal

t [s]

θ [°

]


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3. Test and Evaluation First, functional tests were conducted at the beach to qualitatively determine whether the weight apparatus would perform as intended in the environment in which it will be used. The test consisted of attaching the weight apparatus to the bottom of the SMB and releasing it from a submerged position. The SMB required a 0.5 kg to 1.0 kg mass to dampen perturbations and return the SMB to a vertical configuration during ascent and at the surface. The results proved that the weight apparatus does indeed achieve its intended functions, and showed that it would be worthwhile to continue developing this design.

Static testing was then performed to optimize the mass of the weight apparatus, with this experimental setup

shown in Figure 17. Various masses, mi, were attached to the bottom of the SMB and the corresponding submerged heights of the SMB, hsub_i, were measured. This test was necessary in determining the upper (no more than 40% submerged) and lower (SMB remains upright) limits of the usable mass.

Of the masses tested, the functional range was found to

be between 0.45±0.01 kg and 0.90±0.01 kg shown in Figure 18. The experimental data agreed with the numerical model for all but two points. The two outer masses—0.2 kg and 0.9 kg—that deviated from the model each differed by approximately 3%. This difference can be attributed to the change in the submerged volume as the masses were added or removed, which ultimately affected the buoyant forces acting on the system. The results of the experiment validated the numerical model. A mass of 0.526±0.001 kg was then chosen for further testing as it was readily available and also fell within the operable range.

Because the SMB must also remain vertical after

being perturbed by waves, winds, and currents at sea, a second test was performed to ensure that the chosen mass would allow the SMB to self-correct itself after undergoing disturbances. This experimental setup is shown in Figure 19. In this test, the SMB was released from an angle of 60° to determine whether it would converge back to a stable vertical position, which was set to be 0° ± 10° from the vertical axis. A video was recorded to observe the SMB’s behavior and to determine its angular orientation.

The experimental results are listed in the Table 2 and Figure 20. The deflection angle at 4.2 s was used for

comparative reasons, as this was the experimental time at which the SMB settled. Although the experimental data does not match the numerical model in all categories, the important takeaway here is that the two had the same steady state behavior: the SMB converged and was able to self-correct and ultimately return to a stable position.

Figure 17. Experimental set up for testing mass compared to height submerged.

Figure 18. Mass of weight apparatus compared to submerged height of SMB. Experimental data trends compared to prediction of numerical model.

Figure 19. Experimental setup for surface stability test.

40% SUBMERGED HEIGHT LIMIT


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Finally, ascent time, and thus

velocity, was measured by releasing the SMB from a specified depth, dsub, shown in Figure 21. Ascent completion was determined by the time when the top of the SMB reached the surface of the water. In determining the velocity, it was also assumed that the SMB reached Uterminal almost instantaneously because of t << 1 s acceleration time from the numerical model, thus the equation U = d/t was used. To subermege the SMB, two methods were used: (1) swimming down with the SMB and (2) using a weighted pulley mechanism to lower SMB. From this

testing method, time of ascent data was taken at different depths shown in Table 3.

The data shown in Table 3 suggests that the

SMB without the apparatus ascended at U = 2.4±0.9 m/s, while the attachment decreased it to 0.2±0.1 m/s. However, this data cannot be used to accurately quantify the impact of the weight apparatus on the ascent characteristics due to the

large error margins (37.5% and 50% respectively). Ideally, a fully equipped scuba diver would be hired to descend to various depths (5 m – 15 m) and inflate and release the SMB, and sensors would be used to record the ascent time

for more accurate data. However, resource limitations restricted the extent in which data could be obtained. The

testing methods used here did not allow for data to be obtained at sufficient depths or with reasonable error margins. Therefore, while qualitative data suggests that the SMB ascends at a slower rate, reliable quantitative data could not be obtained to further support it.

V. Final Design End users, marketability, and cost efficiency in addition to function influenced the final product design of the SMB attachment. The weight apparatus was chosen as the concept to improve upon for the final design. To fulfill the design requirement regarding inflation, a small consumer-grade air canister was needed, as can be seen in Figure 22. This 0.046 kg air canister with regulator would

Figure 20. Numerical compared to experimental data for surface stability test.

Table 2. Numerical compared to experimental values for surface stability test

Numerical Experimental Overshoot (°) 1.0±0.1 20±5 θ at 4.2 s (°) -0.18±0.01 2±5 Natural Frequency (ωN) (Hz)

1.08±0.01 0.391±0.002

Figure 21. Experimental setup for ascent time.

Table 3. Experimental ascent data Depth (m) t (s) U (m/s)

Without Weight

Apparatus 0.9±0.3 0.36±0.05 2.4±0.9

With Weight Apparatus 0.30±0.05 1.3±0.5 0.2±0.1

Figure 22. The air canister used in the final design of the capsule to inflate the SMB.


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be housed in a capsule. A user of the SMB would simply purchase a readily available refill canister for under $2 and insert it into the capsule holding the regulator prior to each dive.1 The final design is pictured in Figure 23(a). It is constructed out of ABS plastic, because the material must be lightweight and waterproof for function in typical scuba diving applications. The inside of the capsule hollow to make room for the air canister. All edges are filleted and rounded for safety. A hole on the side of the capsule

allows the air canister to connect to the tube, as shown in Figure 23(b). The top of the capsule is shaped as an inverted dome to increase the amount of drag received by the capsule to further reduce the terminal velocity of the SMB during ascent. At the top of the capsule is a loop, which is used to secure the tube from the air canister to the nozzle in place.

The capsule is 0.171 m from base to height and 0.080 m in diameter. The basic layout of the capsule can be seen

in Figure 23(c). Sizing of the capsule was based on the amount of mass needed to keep the SMB upright and submerged less than 40% of its height. The final mass of the capsule was made to be 0.551 kg. The extra mass was added to ensure the capsule would work with other sizes of SMBs while maintaining the 40% submersion requirement.

VI. Conclusions The final proposed design of the SMB capitalizes on the simplistic functional nature of the weight apparatus

prototype, utilizing the space effectively to implement the air canister. The weight apparatus prototype fulfilled three out of the four design requirements, but with the addition of the canister, all four design requirements were met. Additionally, rather than having created an entirely new SMB, the designed device is an add-on for existing SMBs. This means that the product can be used to supplement SMBs previously purchased by scuba divers, therefore making this final product design a simple but effective option to address the problems currently faced by scuba divers.

In the future, the final design prototype can be fabricated to specification, then tested to experimentally validate

the final design operates as expected. A full set of surface stability and ascent to surface testing would be completed as discussed by this report.

References 1"Lezyne - CO2 Inflators - Control Drive." Lezyne. Lezyne, 2014. Web. 05 Dec. 2014. 2Prusa, Joseph M. "Hydrodynamics of a Water Rocket." SIAM Review 42.4 (2000): 719. Web.

<http://epubs.siam.org/doi/pdf/10.1137/S0036144598348223>. 3"Satellite Applications for Geoscience Education." Satellite Applications for Geoscience Education. N.p., n.d. Web. 04 Sept.

2014. <https://cimss.ssec.wisc.edu/sage/oceanography/lesson4/concepts.html>. 4"XS Scuba Surface Marker Buoy." XS Scuba Surface Marker Buoy. XS Scuba, 2014. Web. 05 Sept. 2014.

(a) (b) (c) Figure 23. (a) A view of the capsule in an exploded view, showing the top and base. (b) A visualization of how the capsule would look connected to a tube connected to the SMB nozzle.

[3] aiaa_improvedsurfacemarkerbuoyforscubadivers

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