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Buoyancy Spacing Implications for Fatigue Damage due to Vortex-Induced Vibrations on a Steel Lazy Wave Riser (SLWR) Dr. Vikas Jhingran and Mr. Heping Zhang, Shell International Exploration and Production, Houston, TX, USA Mr. Halvor Lie and Mr. Henning Braaten, Marintek, Trondheim, Norway Dr.J. Kim Vandiver, Professor, Massachussets Institute of Technology, Cambridge, MA, USA

Copyright 2012, Offshore Technology Conference This paper was prepared for presentation at the Offshore Technology Conference held in Houston, Texas, USA, 30 April–3 May 2012. This paper was selected for presentation by an OTC program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material does not necessarily reflect any position of the Offshore Technology Conference, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Offshore Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of OTC copyright.

Abstract As oil and gas exploration ventures into deeper waters, designing risers with sufficient extreme strength and fatigue life becomes a challenging task. This task is even more difficult in regions with strong currents at great depths. Among the handful of riser concepts that can be used in such conditions, the Steel Lazy Wave Riser (SLWR) concept has shown great promise. The SLWR concept does come with its own share of challenges. When deep ocean currents exist, obtaining sufficient fatigue life due to Vortex Induced Vibrations (VIV) becomes a major design challenge. A critical area of concern from VIV fatigue damage is the buoyancy section on the SLWR riser. Shell Oil Company performed some state-of-the-art experiments in 2011 to study the effects of buoyancy spacing on VIV response. The experiments were performed at the Marintek Ocean Laboratory in Norway with a 38 m (~125 ft) long pipe what was 30 mm (1.18”) in diameter. The buoyancy was simulated using 80 mm (3.15 “) diameter sections. This paper describes these experiments, discusses results and provides design insights on the effective sizing and placement of the buoyancy modules in SLWRs to minimize the fatigue damage caused by VIV. Introduction As Oil and Gas exploration continues to advance into deeper waters and harsher environments, engineers are faced with the daunting task of developing practical riser designs for these new develpments. In recent years, Steel Lazy Wave Catenary Risers (SLWR’s) have provided engineers with riser solutions for a wide variety of challenging environment and field configurations. SWLR’s combine the robustness of Steel Catenary Risers (SCR’s) with the fatigue chararteristics of flexible risers. As offshore oil exploration progresses into unchartered domains, we believe SLWR’s will become the riser configuration of choice for many future projects. There are however great challenges in designing a SLWR system, particularly if the site specific MetOcean data indicates strong currents at great depths. The SLWR system, as shown in Figure 1, relies on a buoyant section in the riser to provide flexibility and enhanced fatigue life, particularly in the touchdown area. Typically, the buoyancy on the riser is staggered and not continuous to minimize time of installation1. If however, the buoyant region of a SLWR is subject to strong currents, fatigue due to Vortex-Induced Vibration may become important even if the non-buoyant regions of the riser have VIV suppression on them. There are two reasons for this. First, the variation in depth over the buoyant region is typically small, making it possible for the entire region to be exposed to a current of uniform magnitude with little directional variation in the current profile. Second, the buoyant region typically has very low tension resulting in higher local curvature response due to VIV than other regions of the SLWR. This results to higher fatigue damage in the buoyant region compared to other areas of the SLWR for the same diaplacement amplitude of VIV response. 1 In this paper, the authors refer to the section of riser pipe with buoyancy modules (continuous or intermittent) as the “buoyant region” of the SLWR.

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Figure 1 - A Schematic of a Steel Lazy Wave Riser

There exists little previous research on the VIV response of pipe with staggered buoyancy modules. Results from model tests performed at Marintek in a rotating rig are presented in Lie et al [1]. Also Li et al [2] and Fu et al [3] present experimental results from model tests of riser models with staggered buoyancy modules. Peoples and Vandiver [4] also analyzed data from experiments with staggered buoyancy modules and provided some insight into how much buoyancy coverage was required so that the VIV from the larger diameter buoyancy would dominate the response. Insights obtained from this body of previous work indicates that the resulting VIV amplitude for a riser with staggered buoyancy modules may depend on the ratio of the length of the buoyancy segments to the length of the gaps between two adjacent buoyancy segments. To further understand these VIV concerns, in 2011 Shell Oil Company undertook a hydrodynamic test program of riser models subjected to vortex-induced vibrations (VIV) with configurations corresponding to the buoyant section of a SWLR. These experiments resulted in data at Reynolds numbers greater than 200,000 (when computed using the diameter of the buoyancy module) and provided the best available data for the VIV design of SLWR’s. The tests were conducted with a 30 mm (1.18 in) OD riser model with 80 mm (3.15 in) OD buoyancy elements. Five different gap ratios, defined later in this paper, were studied in an effort to determine a range for this parameter that leads to the smallest VIV fatigue damage (and hence an optimal riser design with respect to VIV fatigue). The tests studied VIV response of the staggered buoyancy configurations only in uniform currents, reflecting the worst-case but likely real-world scenario for SLWR’s. The Shell Experiments The Shell experiments were performed in The Ocean Laboratory at MARINTEK. The Ocean Laboratory is 50 m wide and has a length, from the wave maker to the intersection between beach and water surface, of 80 m. The depth of the basin is 10.0 m. The basin is fitted with an adjustable floor of area 48 m by 42 m. This makes the depth over the whole area adjustable from 0.0 m to 8.7 m. MARINTEK has previous experience testing a 38-m long horizontal riser model attached to a test rig via universal joints (see [1] for more details). This experience helped develop the setup used for the Shell experiments. For these tests, a new test rig was fabricated using a 40.5 m long horizontal truss beam, which was suspended from the gondola/crane system in the Ocean Basin Laboratory. To this truss beam, two vertical pendulums were attached with clump weights located at the lower end of each pendulum. Then the riser ends were attached to these clump weights via universal joints. Figure 2 presents a schematic drawing of the test set-up.

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Figure 2 - Test setup at the Marintek Ocean Tank facility

The experiments used a 38 m (~125 ft) long, 30 mm (1.18 in) OD pipe as the riser with a 41 cm (15.75 in) long, 80 mm (3.15 in) OD buoyancy modules (see Figure 3). The inner core pipe was fabricated using fiberglass material and fitted with dense instrumentation that provided measurements of bending strain and accelerations along the riser model in the in-line (IL) and cross-flow (CF) directions. The buoyancy modules were fabricated from polyurethane half cylinders, which were clamped in pairs around the 30mm riser model and secured in place using locking clips. The two halfs fit snugly over the inner core pipe and were contrained from slipping relative to each other by pins, which protruded from one half cylinder into mating holes in the other half-cylinder, as shown in Figure 4. Cavities were left in the buoyancy halfs to accomodate protrutions of the accelerometers in the inner pipe. More details about the experimental setup and model pipe can be found in Lie et al [5].

Figure 3 - (a) The riser and bouyancy module (b) The riser during experiments with gap length equal to the buoyancy

module lengths

Figure 4 – The buoyancy modules were fabricated as half cylinders with a central grove to accommodate the riser model. The test matrix for the staggered buoyancy experiments consisted of 45 runs at varying tow speeds and coverage of buoyancy sections. Only uniform flow was tested for these configurations. Figure 5 shows a schematic of the riser pipe with buoyancy

(a) (b)

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sections. The length of the buoyancy sections, denoted as Lb, and the gaps between buoyancy modules, denoted as Lc, were measured as multiples of the length of one buoyancy module i.e. Lc=2 denotes a gap equal to the length of two buoyancy modules. In these experiments, the ratio of Lc/Lb, which is the length of the gap divided by the length of the buoyancy segment, was a key variable.

Figure 5 - Definition of Gap lengths and Buoyancy Segment Lengths

!Table 1 provides details of the various configurations that were tested. The configuration matrix was populated based on the current understanding of the response of pipe with two different diameters. Instead of just a number, the authors state Lc/Lb

values as modulesbouyancy ofnumber assection buoyancy ofLength

modulesbuoyancy ofnumber as gap ofLength =

b

c

LL . This has the advantage of identifying the

length of the buoyancy and gap segments in addition to the percentage of buoyancy coverage in the buoyant region of the riser. Table 1 – Configurations of Buoyancy modules tested as part of the Shell experiments.

Number of Tests Test Configuration Velocity Profile 9 Configuration 1 - Lc/Lb =5/2= 2.5 Uniform 9 Configuration 2 - Lc/Lb = 3/1=3.0 Uniform 9 Configuration 3 - Lc/Lb = 3/2=1.5 Uniform 9 Configuration 4 - Lc/Lb = 1/1=1.0 Uniform 9 Configuration 5– long buoyancy elements, Lc/Lb = 2/2= 1.0 Uniform

"#$%&'$!The buoyancy element designs in SLWR’s are greatly impacted by fatigue damage considerations. The authors have thus concentrated on frequency and curvature measurements and not displacement measurements since fatigue response is governed by curvature and frequency of response rather than displacement. Further, only the response in the Cross-Flow (CF) direction is studied in this paper. !Response - Frequency Since the buoyancy region of an SLWR consists of a staggered configuration with two cylinders of different diameters, lift forces on the bare riser will “compete” with lift forces from the buoyancy sections at different vortex shedding frequencies. The riser will experience multiple excitation frequencies even in uniform flow. In our experiments, the ratio between buoyancy element diameter and riser diameter is 2.67. The non-integer ratio prevented the bare riser vortex frequency from being a multiple of the vortex shedding frequency from the buoyancy elements. This is an important consideration in design. If a higher harmonic of the buoyancy vortex shedding frequency is equal to the shedding frequency from the bare riser, it may enhance the total VIV response of the SLWR. For example, if the ratio of the pipe-to-buoyancy diameter is 3, the frequency of the third harmonic of the excitation from the buoyancy elements will match the frequency of the first harmonic excitation from the pipe, potentially resulting in greater fatigue damage. Figure 6 presents the power spectrum of cross-flow curvature close to the midpoint of riser for test 6047. The riser model was towed at a uniform speed of 1.0 m/s and Lc/Lb=1/1 for this experiment. Two principal response frequency regions are observed, the first around 1.5 - 1.65 Hz and the second from 5.3 – 5.65 Hz. The lower frequency response region in Figure 6 indicates the response of the riser due to VIV excitation generated in the buoyancy segments. It corresponds to a Strouhal number of 0.12 to 0.1325, which is lower than typically observed for bare pipe for reasons discussed later in this paper. The higher frequency region is the response from the bare riser section and the Strouhal number associated for this response is between 0.16 and 0.17. These calculation assume a relationship of the form, !!!"!!!#!$!.

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Figure 6 - Two peaked power spectrum for a riser with intermittent buoyancy modules

To study the response frequencies in more detail, we high and low-pass filtered the curvature signal with a cut-off frequency equal to the average of the theoretical Strouhal frequency for the buoyancy part and the riser part. This separates the response associated with the buoyancy modules, the low frequency component of the response, from the response associated with the bare riser, the high frequency component of the response. This was done for all the 45 experiments that were part of the testing program. At the location with highest RMS CF curvature response along the length of the riser, Figure 7 presents the frequency, in hz, of the peak in the low frequency curvature spectrum and the frequency, in hz, of the peak in the high frequency curvature spectrum. Each Lc/Lb value has two associated curves in Figure 7, one representing the frequency of the excitation from the riser and the other representing the frequency of excitation from the buoyancy section. Also shown in Figure 7 are the theoretical Strouhal frequencies for the buoyancy part, fst buoyancy (solid line) and the riser part, fst riser (dashed line), using a Strouhal number of 0.155. Figure 7 shows the dual nature of the VIV response for a riser with staggered buoyancy. There is a “competition” between the bare pipe and the buoyancy segments to control the response of the pipe.

Figure 7 - The response frequency, as a function of velocity, due to excitation in the bare region and the buoyancy

region To infer which frequency “controls” the response, we plotted the frequencies shown in Figure 7 that are associated with the largest RMS response in the curvature spectrum. For each Lc/Lb configuration in Figure 7, the frequency corresponding to the greater of the low frequency (buoyancy) or high frequency (riser) RMS curvature response was selected. This was obtained for all Lc/Lb values and at various velocities. The results are shown in Figure 8 where each curve represents a different Lc/Lb value. Also shown are the theoretical Strouhal frequencies for the buoyancy part, f80 (solid line) and the riser part, f30 (dashed line), using a Strouhal number of 0.155. Figure 8 provides guidance on when the “switch” occurs from the bare pipe dominating the response to the buoyancy section dominating the response. Since the diameter of the buoyancy elements did

Buoyancy Pipe Response

Bare Pipe Response

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not change in these experiments, this figure can be used to infer the pipe-to-buoyancy length ratio when the response “switches” from being controlled by the pipe to being controlled by the buoyancy modules. We see that the response for Lc/Lb=5/2 and Lc/Lb=3/1 is dominated by the bare riser part. The high frequency for 3/1 at the lowest speed is due to very little response that is within the noise level. For Lc/Lb=2/2 the response is dominated by the buoyancy part while for Lc/Lb=3/2 the peak frequency is close to either the f80 or the f30 depending on velocity. Lc/Lb=1/1 seems like a contradiction to the above explanation but the authors believe that this is a special case and an explanation is provided below. The above observations can be explained in the following manner. It is reasonable to assume that when two excitation frequencies are “competing” in a flexible riser with closely spaced modal frequencies, the “winner” is determined by the excitation frequency that puts in the larger force. The excitation force due to VIV can be defined as vlift ClDVF 2

21 != . Since

the magnitude of the lift forces are dependent on the diameter, we would expect the switch between the “buoyancy controlled regime” and the “riser controlled regime” to occur in the neighbourhood of Lc/Lb=2.67. This is what we see in Figure 8. Lc/Lb=2/2 is controlled by the buoyancy. Lc/Lb=3/1 is controlled by the riser. There is no clear “winner” in ratios in between 1.0 and 3.0 as the excitation from the buoyancy and the bare riser seem to be equally pronounced. Lc/Lb=1.0 seems like an anomaly but we believe this is due to the small length-to-diameter ratio of the buoyancy elements (L/D~5.0). The hydrodynamic excitation for this buoyancy configuration seems to be characterized by a lower Strouhal number and lower RMS curvature response (see Figure 12 and Figure 9 ). Thus for experiments where the Lc/Lb=1/1, the dominating frequency response does not indicate a “winner” since the RMS curvature response is reduced resulting in the lowest fatigue damage of all the combinations tested during these experiments. Both these response properties are discussed in detail in later sections of this paper.

Figure 8 - The frequency associated with the highest peak in the strain spectrum

!!!"#$()*$#!+!,%-./'%-#!The second, and more significant, response that affects fatigue is curvature. Figure 9 presents the maximum RMS curvature along the length of the riser, in m-1, in the cross-flow direction. This is shown for all Lc/Lb values and for various velocities. As can be seen from the figure, Lc/Lb=1/1 has the lowest curvatures for the tested cases while Lc/Lb=5/2 and Lc/Lb=3/1 have the highest curvature measurements. These results are very significant. An arrangement of equal proportions of buoyancy elements and bare riser will result in the least amount of curvature response in the pipe. The comparison of the RMS curvature response for Lc/Lb=2/2 and Lc/Lb=1/1 is surprising since both indicate similar coverage patterns of buoyancy modules except for different length-to-diameter ratios of the buoyancy module. This seems to indicate that small L/D ratios for buoyancy modules have a significant impact on the Strouhal number associated with the excitation but also on the overall magnitude of the curvature response, possibly in part because lower response modes are excited.

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Figure 9 - Maximum observed RMS Curvature with increasing velocity

Damage index To examine the influence of fatigue on the measured response amplitudes, frequencies and modal curvatures, we use a damage index based on the measured curvature. !

mzfDI !"= %!&'()(!*"+!

!The power of three in the equation assumes an S-N curve with a slope of three. This yields an effective quantifier of fatigue damage that is independent of stress concentration factor, material Young’s modulus or S-N curve intercept. As shown in Figure 6 the power spectrums for curvature signals are multi-peaked. To calculate the fatigue damage from these responses we use an approach similar to the one described in [6]. The prediction of the fatigue damage rate is based on use the combined spectrum approach i.e. the fatigue damage rate is estimated using combined curvature RMS and corresponding zero crossing frequency into the equation above. This approach will overestimate the fatigue damage. Jiao [7] has developed a correction factor ! from two independent narrow-banded Gaussian processes. The fatigue damage can be calculated as the fatigue damage rate using the combined spectrum approach and multiplying with the correction factor !. Figure 10 presents the maximum RMS damage index in the cross-flow direction for different Lc/Lb ratios and velocities. We find the same trends for the damage index as for the curvature results. The configuration with Lc/Lb=1/1 has the lowest damage index and is hence the preferred configuration based on these tests.

Figure 10 - Damage index shows the least damage for Lc/Lb=1/1

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The authors want to highlight that the fatigue damage changes by an order of magnitude between the configuration with the lowest damage (Lc/Lb=1/1) and the configuration with the highest damage (Lc/Lb= 3/1 or 5/2). This magnitude of the variation in fatigue damage could easily mean the difference between an acceptable design vs one that does not meet the fatigue requirements of a project. Further, it could also lead to expensive and installation intensive VIV mitigation techniques like strakes on the buoyancy modules and VIV mitigation coverage over bare riser in this buoyant region of the SWLR. Buoyancy element length effects Previous studies [8] show the Strouhal number for short stout pipes being lower than for long slender pipes (Figure 11). This suggests that for very short buoyancy modules, the Strouhal number should be affected by the length of the buoyancy modules. Short buoyancy modules, like short stout pipes, will have lower Strouhal number exciting lower response modes. This results in lower fatigue damage. Though similar studies have been conducted to verify this Strouhal number trend, they were not at very high Reynolds numbers and / or were conducted with rigid cylinders. The current experiments are the first attempt that the authors are aware of to verify this for flexible pipes at relatively high Reynolds number.

Figure 11 - The change in Strouhal number with increasing L/D ratio of pipe [5]

Figure 12 presents the normalized response frequency,

UDff osc=ˆ , for the different tested cases. In all these cases,

oscf represents the frequency of excitation generated in the buoyancy segments and D represents the diameter of the buoyancy modules (80 mm). The effect of buoyancy module length can be investigated by looking at the two curves corresponding to Lc/Lb=1/1 and Lc/Lb=2/2. The aspect ratio ( D

L ) for 1/1 configuration is 5 while it is 10 for the 2/2 configuration. The normalized response frequency for 2/2 is higher than 1/1 for all towing velocities. The effect of buoyancy element length could also be seen in Figure 9 presenting the maximum RMS CF curvature where 1/1 has lower response than 2/2.

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Figure 12 - The measured normalized frequency was consistantly lower for Lc/Lb=1.0

This result has important consequences for SLWR designs. The authors suggest using smaller length buoyancy modules for enhanced fatigue performance of an SLWR. The suggestion has to be tempered against installation implications. Typically, smaller lengths of buoyancy modules will result in slower installation times, causing installation costs to go up. However, the authors point out that if the SLWR design is unable to meet design fatigue life requirements; engineers do have the option of using smaller buoyancy segments to enhance VIV fatigue life with little or no change in the design of the riser. Conclusions The authors believe that SLWRs are going to provide a practical solution for many challenging deepwater design in the years to come. A key aspect of the SLWR design will be VIV related fatigue damage in the section of the riser with buoyancy modules. The depth in this section typically does not change and it is usually difficult to put VIV mitigation in this section of the riser. This paper reports new results using data from recent experiments conducted by Shell Oil Company and addresses some important characteristics of the VIV response of SLWR’s. Based on the results reported in this paper the authors make the following conclusions:-

1) During VIV analysis of an SLWR configuration, the use of average diameter, a common assumption for VIV fatigue analysis, to model the SWLR in the buoyant region may not be accurate. This assumption does not consider the competition between modes generated in the buoyancy region and bare riser regions. It also does not account for the change in Strouhal number in case of small length-to-diameter ratios of the buoyancy modules.

2) The buoyancy modules and bare riser regions “compete” for the VIV response of the SLWR. The buoyancy modules should be designed such that its VIV response of the SLWR is dominated by the excitation generated in larger diameter, buoyancy segments rather than the smaller diameter bare riser segments. This leads to lower structural modes of the SLWR being excited resulting in lower fatigue damage of the SLWR. A rule of thumb for the largest gap between buoyancy modules before the bare riser starts dominating response is

G

B

B

G

DD

LL

! , where

LG=Length of Gap, LB=Length of Buoyancy Module, DG=Diameter of riser in the Gap region, DB=Diameter of Buoyancy Module

3) The design implications of the statement in 2) above include that for a given volume of buoyancy needed for an SLWR application, choosing the diameter of the buoyancy can have important consequences. If the computed diameter of the buoyancy module is such that the equation in 2) is not satisfied, the length of the buoyancy should be increased till the diameter of the buoyancy module satisfies the equation in 2) above. This will ensure that the response is controlled by the excitation from the buoyancy modules and not by the excitation from the bare riser. The fatigue advantages of this have been discussed in the body of this paper. This consideration has to be weighed against the practicality of having more buoyancy modules during installation of the SLWR’s.

4) After the length and diameter of the buoyancy needed has been determined, the most effective configuration, other things remaining equal, is to use short buoyancy modules separated by gaps. A buoyancy module length-to-diameter ratio of 5.0 or smaller reduces the response frequencies resulting in lower fatigue life. In other words, for buoyancy

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modules with length-to-diameter ratio of 5.0 or lower, a configuration of 1B-1G, where B=Buoyancy module and G=Gap, is preferable to 2B-2G even though the percentage of buoyancy coverage provided by the two configurations is the same.

Acknowledgements The authors would like to thank Shell Operating Company (SepCo) and Shell International Exploration and Production (SIEP) for allowing the authors to publish these results. References [1] A.D. Tim, H. Braaten, H. Lie, M.A. Tognarelli. “Experimental Investigation of Vortex-Induced Vibration of Long Marine Risers”. Journal of Fluids and Structures, 2005: p.335–361. [2] Li et al, “Experimental Investigation on Vortex-induced Vibration of Risers with Staggered Buoyancy”, OMAE, Rotterdam, 2011 [3] Fu, S., Ren, T., Li, R., Wang, X., "Experimental investigation on viv of the flexible model under full scale Re number", OMAE2011-49042, Proceedings of the ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering OMAE2011 June 19-24, 2011, Rotterdam, The Netherlands [4] Lie, H., Braaten, H., Jhingran, V. G., Sequeiros, O. E., Vandiver, K., "Comprehensive riser viv model tests in uniform and sheared flow", OMAE2012-84055, Proceedings of the ASME 2012 31th International Conference on Ocean, Offshore and Arctic Engineering OMAE2012, June 10-15, Rio de Janeiro, Brasil [5] Vandiver, J. K. and Peoples, W., The Effect of Staggered Buoyancy Modules on Flow-Induced Vibration of Marine Risers", Paper No. OTC 15284, Proceedings of 2003 Offshore Technology Conference, Houston, May 2003 [6] Lie, H.and Fylling, I.J., ”Evaluation of Methods for Fatigue Analysis of Offshore Mooring Lines”, 10th Offshore South East Asia Conference & Exhibition, OSEA, Singapore, 1994 [7] Jiao, G., “Reliability Analysis of Crack Growth under Random Loading Considering Model updating”, Dr. ing. Thesis, Division of Marine Structures, NTH, Trondheim, 1989 [8] Gouda, B.H.L., “Some Measurements of the Phenomena Vortex-Shedding and Induced Vibrations of Circular Cylinders”, Technische Universitat Berlin, Report DLR-FB 75-01, 1975