NPO VNIIstroidormash: Soviet Construction Equipment Technology

On my companion site, I have posted several articles on Soviet (and after that Russian) pile driving equipment, such as diesel hammers, concrete pile cutters, and vibratory and impact-vibration hammers.  These are very specialised topics, even by construction industry standards; here I want to present some photos of more general interest to you heavy equipment fans.  The Soviet Union was known for its commitment to heavy manufacturing and construction equipment like this is certainly a big part of that.

NPO VNIIstroidormash is the Soviet name for the Moscow-based institute which designed and tested the equipment shown below.  The name means the All-Union Scientific Research Institute of Construction and Road-Building Machinery.  It was put together in 1975, and survived past the end of the Soviet Union in 1991 as a share society, i.e., a privatised corporation.  In addition to the pile driving equipment which got me involved with the organisation, it designed many other types of equipment, and the best way to show this follows, from their catalogue produced around 1986.

DZ-110A-1 Bulldozer with laser-beam steering and control system. Surface-working accuracy +-5 cm at 10-400 mm distance from the laser source. Such a set-up is common today; at the time it was not.
DZ-110A-1 Bulldozer with laser-beam steering and control system. Surface-working accuracy +-5 cm at 10-400 mm distance from the laser source. Such a set-up is common today; at the time it was not.
Similar, laser-levelled concept with a DZ-122A-13 motor grader.
Similar, laser-levelled concept with a DZ-122A-13 motor grader.
EO-4125 excavator. The excavator is probably the single most versatile and important earth moving machine on a construction site. This one sported servo-controlled valves, which makes current excavators much easier to operate than their older counterparts.
EO-4125 excavator. The excavator is probably the single most versatile and important earth moving machine on a construction site. This one sported servo-controlled valves, which makes current excavators easier to use than their older counterparts.
Excavators are versatile in that things other than the usual bucket can be mounted on the boom. In this case, the MTP-71A excavator has an extended backhoe that is used for large swing radii and canal digging. It's mounted on rubber tyres (the one above is on tracks) for softer soils; it's also easier to transport on roads.
Excavators are versatile in that things other than the usual bucket can be mounted on the boom. In this case, the MTP-71A excavator has an extended backhoe used for large swing radii and canal digging. It’s mounted on rubber tyres (the one above is on tracks) for softer soils; it’s also easier to transport on roads.  To increase the effective counterweight it sports outriggers.
EO-3323 excavator, also mounted on tyres with outriggers. The red bucket on the end has a capacity of 0.75 cu.m.
EO-3323 excavator, also mounted on tyres with outriggers. The red bucket on the end has a capacity of 0.75 cu.m.
Turning to cranes, this is a 12.5 (metric) ton hydraulic truck crane. Very useful for light lifting, they're fairly common on construction sites and other places.
Turning to cranes, this is a 12.5 (metric) ton hydraulic truck crane. Very useful for light lifting, they’re fairly common on construction sites and other places.
40-ton truck crane, another versatile tool.
40-ton truck crane, another versatile tool.

Our business used these often for the assembly of our larger hammers, but sometimes things didn’t go according to plan.

For really heavy lifts, Vulcan could have used this for its biggest products. Cranes such as this were used in the early 1980's for the modification of its biggest hammer.
250-ton crane.  For really heavy lifts, Vulcan could have used this for its biggest products. Cranes such as this were used in the early 1980’s for the modification of its biggest hammer.
Vibration roller for compaction. These machines are not really intended for deep compaction of soils but surface smoothing, which is necessary when building roads and airfields.
DM-476 vibration roller for compaction. These machines are not really intended for deep compaction of soils but surface smoothing, which is necessary when building roads and airfields.
DZ-140 motor grader, used for final levelling of roadways before smoothing and paving. The blade is 4.8 m long.
DZ-140 motor grader, used for final levelling of roadways before smoothing and paving. The blade is 4.8 m long.
A skid steer loader, better known on American jobsites as a
TO-31 skid steer loader, better known on American jobsites as a “Bobcat” after the popular American brand. Maybe they should have named this a “Siberian Tiger.”
A bulldozer-ripper. Most people connect bulldozers with moving soil, but this one is designed to break up rock for removal.
A bulldozer-ripper. Most people connect bulldozers with moving soil, but this one is designed to break up rock for removal.
Computer aided design, 1980's style: VNIIstroidormash's computer room.
Computer aided design, 1980’s style: VNIIstroidormash’s computer room.
VNIIstroidormash's library.
VNIIstroidormash’s library.
VNIIstroidormash's female ski team.
VNIIstroidormash’s female ski team.

Our family business first connected with the Institute in 1988, and our contacts continued for the next six years.  Sometimes things got strange but we discovered an organisation that put out some very good designs for construction equipment.  Unfortunately the Soviet manufacturing organisation was not up to proper quality control, especially in the civilian sector, and that weakness was one of those which ultimately brought the Soviet Union down.

Maybe No One in the U.S. Really Likes Democracy Anymore

Jeet Heer thinks that the right has given up on democracy:

Public-opinion polling shows that Trump’s low opinion of American elections has practically become Republican Party orthodoxy. According to a Reuters/Ipsos poll released on Friday, Republicans have an “unprecedented” level of “concern and mistrust in the system.” Roughly 70 percent of Republican voters believe that if Hillary Clinton wins the election, it’ll be due to fraud. In both this poll and an NBC News/SurveyMonkey poll, only half of Republicans say they’d accept a Clinton victory. (In the latter poll, by contrast, 82 percent of Democrats said they would accept a Trump victory.)

But they’re not alone:

Those aren’t the only political data that set young millennials apart from their elders. According to an exhaustive report by political scientists Roberto Stefan Foa and Yascha Mounk in the Journal of Democracy, young people today are considerably more authoritarian and antidemocratic by attitude and temperament than any other generational cohort, especially baby boomers. Only 30 percent think that it’s “essential” to live in a country with a democratic system of government, and a terrifying 24 percent actually think that a democratic system of government is a bad thing. Only 32 percent of millennials think that it’s “absolutely essential” that “civil rights protect people’s liberty.” According to a Pew Research Center report, 40 percent of millennials want the government to ban “offensive” speech.

Does anyone really care if we have democratic process any more?  Or is it just a matter of winners and losers?

To this I have two observations:

  1. Our country’s elites have been raised in an environment where they don’t know what real freedom is, and that’s trickled down in our society, especially with the millennials.
  2. Our system is based on a stronger consensus than we have now; when it breaks down, we have a mess.

We Should Challenge the Legitimacy of Our System’s Outcome

Donald Trump’s mushy statement about his acceptance of the outcome of the Presidential election has many up in the air.  Such a knee-jerk reaction–driven by a system which has been so successful for so long that people take it for granted–needs to be tempered by a reality check.

First: it’s not the first time the results of a Presidential election in the U.S. haven’t been accepted.  Al Gore certainly did not, and the left never has accepted the results of the 2000 election.  John Kerry turned his nose up at 2004.  The left is fearful that Trump’s supporters will turn to armed insurrection, but problems like that are what the police and military are for, and you should have thought of that before weakening the military and trashing the police the way Barack Obama has.  (Remember the admonition of Septimus Severus to his sons: stick together, pay the troops, forget about the rest…)

In any case, it never occurs to anyone that a nominating system that produces two major party nominees going into the final sprint with negative favourable poll numbers  is in serious trouble.  Part of the angst of this election is the unappetizing choice in front of us.  But situations like this are opportunities to take a hard look at why we’re in this mess, and much of the answer to that question is the system we have to start with.

Since these are the days when people come out of the closet on a variety of things, let me do it on this subject: ever since I was a kid, I have never liked the presidential system we have, and always preferred a parliamentary one.  This comes from reading subversive books, and in a country where moving a county line is the local equivalent of a military coup, that’s not an easy belief to hold.

Evangelical Christians (at least the ones who haven’t turned into BDS idiots) can look to Israel as an example of a parliamentary democracy.  The president is a figurehead and every prime minister has to form a government from a coalition of parties to form a (hopefully) majority in the Knesset.  That includes the current Prime Minister, Benjamin Netanyahu.  We hear about the orthodox and ultra-orthodox Jewish parties; they get a seat at the table because they elect representatives to the Knesset and, through the wheeling and dealing the Middle East is famous for, get a place in the government.

In a multi-party parliamentary system, conservative Christians (assuming they could pull their act together, form a decent party, and get proportional representation) could pitch the GOP and negotiate on their own.  And that’s true with many other groups as well.  As it stands now, every four years we have to bet the store on a candidate who may not be the most satisfactory one to represent our interests.  If we lose, we’re stuck with the results.  People who criticise Christians who support Trump need to think about that; we’re facing the abyss with the other candidate.

And I’m not the only one who has pointed out the rigidity of this system.  Matthew Yglesias of Vox did the same thing from a leftist viewpoint in his piece “American Democracy is Doomed:”

The idea that America’s constitutional system might be fundamentally flawed cuts deeply against the grain of our political culture. But the reality is that despite its durability, it has rarely functioned well by the standards of a modern democracy. The party system of the Gilded Age operated through systematic corruption. The less polarized era that followed was built on the systematic disenfranchisement of African-Americans. The newer system of more ideological politics has solved those problems and seems in many ways more attractive. But over the past 25 years, it’s set America on a course of paralysis and crisis — government shutdowns, impeachment, debt ceiling crises, and constitutional hardball. Voters, understandably, are increasingly dissatisfied with the results and confidence in American institutions has been generally low and falling. But rather than leading to change, the dissatisfaction has tended to yield wild electoral swings that exacerbate the sense of permanent crisis.

Voter fraud is certainly a possibility this time around.  But the core problem of our system is that the system has delegitimised itself through its own rigidity.  We can either fix this problem or hope that our thin blue and green lines will hold when things melt down.  But crying about people who don’t automatically accept the results isn’t the answer; changing the system to produce better results is.

NC Political Firebombing Not a Recent First

It’s scary, all right:

Gov. Pat McCrory Sunday called the weekend firebombing of a North Carolina Republican headquarters “an attack on our democracy,” while one GOP official called it an act of “political terrorism.”

In a tweet, Republican presidential candidate Donald Trump blamed “Animals representing Hillary Clinton and Dems in North Carolina.”

Hillsborough police said somebody threw a bottle of flammable liquid through the window of Orange County’s GOP headquarters, setting supplies and furniture ablaze.

But not without precedent:

Just 5 days before the election, at 3a.m. on October 30th, all of the front windows of the Cindy Sheehan for Congress campaign offices were shattered. Although staffers had been in the office less than an hour earlier, no one was in the building at the time of the incident. No one was hurt and there were no witnesses. Cindy Sheehan is a candidate for Congress in California’s 8th Congressional District race against incumbent Nancy Pelosi (D-CA).

“It seems to have been a calculated intimidation tactic,” said Tiffany Burns, the Cindy for Congress campaign manager. “One of our computers was stolen, but no other property was taken from our offices and no surrounding buildings were targeted. Clearly they wanted to both frighten us and to gather information.” Total damage to the campaign office is currently estimated at more than $5,000.

As I said, thugocracy isn’t fun…not for anyone.

A Little Lesson in Subsidarity

One of pot shots that Hillary Clinton and her operatives made at conservative Catholics is that they used terms like “subsidarity” that no one understood. Since they may be right about that, I think an illustration is in order.

Many of you know that I teach Civil Engineering. Six years ago, my department head (who is from Kenya) and his first assistant (who is from the Cameroon) sat me down and asked me to obtain my PhD so I could teach more courses. I agreed and six years later, as W.H Auden said about Tolkien, at the end of the quest, victory.

In the course of the conversation, my department head brought up the subject of why potholes don’t get fixed in Africa the way they do here. (I know we have issues here.) His explanation was this: here, the local authorities (city, county, state) maintain the roads and, since they’re closer to the problem, they have greater incentive to fix it. Back home, decisions are made in the capital, and since they’re far away from the roads, they don’t have a pressing interest, and the potholes remain. That’s probably the best illustration of the concept of subsidarity—which seeks to push decision-making down to the lowest level—that I’ve heard.

Roman Catholicism—especially in its Ultramontane form, which has been the norm since the Restoration—is not the most suitable vehicle to promote the idea of subsidarity. It’s a good theological concept, but the structure of the church works against it.

As far as Hillary Clinton is concerned, truth be told, her problem with subsidarity isn’t that she doesn’t understand it. Her problem is that she doesn’t like it. Her idea—one that has been obvious since Arkansas’ educational “reforms” in the 1980’s—is that power and decision-making be concentrated at the top. People who support subsidarity are political enemies, which is a big reason she wants a “Catholic Spring.”

As far as how two Africans got a Palm Beacher like me to pursue a PhD, it’s another sign that, in engineering, we really do have change we can believe in.

Americans Aren’t the Only Ones to Choose Between “Bad” and “Really Bad”

All of the blubbering and whining going on about how Americans (and especially Christians) are somehow criminal to vote for a certain candidate needs to be put in this perspective, from a 2013 post:

A few months ago, when the Iranians elected themselves a new president, I asked an Iranian friend what he thought of the election.  His response was simple: the Iranian people had a choice between bad and really bad in the election and chose only bad.

Let me ask this: have any of our self-appointed moral compasses in the Christian community ever gone to Iran to advise our brethren there not to vote for a certain candidate because he favours continuing forcing  women to wear the hijab, or hanging homosexuals from construction equipment, or supporting the nuclear weapons program?  Of course not; none of these people would even try to get past Iran’s security system to make this appeal.  And most of them are clueless about societies where these kinds of decisions are a part of daily survival.

The difference between Iran and the United States when it comes to elections is that nominations in Iran are managed by the ruling Islamic system, where here nominations are managed by the stupid nominating system we have.  And the DNC, by tilting the table towards Hillary Clinton, showed that the ayatollahs in Tehran have met their match when it comes to management.  Be that as it may, we have the absurd situation where both major parties have nominated candidates that most Americans don’t like, and that’s a stupid nominating system.

Nine years ago I made it clear that I cannot vote for Hillary Clinton.  That hasn’t changed.  If those who cannot understand the limitations of electoral process–ours and others–don’t understand that, there’s not much left to say.

Our Elites’ Snotty Attitudes, Then and Now

Wikileaks’ revelations that Hillary Clinton and her operatives take a dim view of social conservatives–following her characterization of large portions of the population as “deplorables”–has ignited a great deal of anger.  As someone who started out life growing up with the elites, I think some perspective is in order.

Let me start by putting up something that’s been on this website since 2004.  It comes from my Around the Island post about Palm Beach, and it goes like this:

Below: “There’s a hole in my bucket…” Fourth graders at Palm Beach Day School perform a satire on “hillbillies” called “Appalachian Legend” during Stunt Night 1969. Attitudes from the “coasts” about “flyover country” in the U.S. have been deep seated for a long time; stage productions like this only reinforced that. It’s fair to say that, if the “Religious Right” had fully grasped the contempt they were held in when the movement first got going in the late 1970’s they would not have started the Moral Majority: they would have started a revolution.

Haughty attitudes of our elites towards the rest of the population aren’t new; they’re as old as class differences.  So why didn’t the revolution I thought would be a logical outcome (then, at least) not happen?  There are several reasons:

  1. Our elites had better taste and manners then; they knew better than to rub the rest of the population’s face in their perceived superiority.
  2. We lacked the instant means of communicating contempt we have now.
  3. Most of the “moral majority” didn’t see the difference between their values and those at the top as class based.   That was simply false; the top of our society had been lost to the fervent Evangelicalism for a long time, being steeped in either Main Line Christianity or Judaism.
  4. Some actually did, but didn’t care; they felt that those at the top would go to hell for their lack of belief and they would not.  That kind of “remnant” mentality was very deep in Evangelical Christianity, especially in the South.  One result of the political activity of the last forty years or so is the erosion of that mentality.
  5. Others sensed it, but were too ashamed to admit it, because it would imply those who opposed them were better than they were.  They were and are the aspirational types; much of the impetus for political involvement has come from these people.
  6. Income inequality has increased since that photo was made; the gap between the elites and the Appalachians has grown significantly.

That leads me to some observations about the present:

  • I think it strange that the standard-bearer of those who seek a revolution is a billionaire; it’s one of those bizarre American things.  But it’s the aspirational way: those who idolize Trump project their own aspirations into his own success, which is very common in our society.
  • On the other hand, aspirational people are a threat to the existing power holders, which is why Hillary Clinton and her operatives feel about them the way they do.  Elites, then and now, prefer corporatism.  And that’s ironic too for a bunch whose ideological roots are in 1960’s radicalism.
  • As far as her attitudes towards social conservatives is concerned, what we’re headed for under her idea is a “two-tier” religious structure where certain churches and religious organizations are “acceptable” and certain ones are not, with legal disabilities following.  That was the case in Nazi Germany with the “Confessing Church,” in the Soviet Union, and is the case in China, although the Three-Self Church is showing many signs of life.  Her idea that Roman Catholicism is an “élite” religion (as opposed to Evangelicalism) has a strange feel to it.  Going from Episcopal to Catholic was a drop in social level in the 1970’s, but the Main Line churches have lost most of their relevance even at the top.
  • Trump’s crudity is unsurprising, especially for someone raised in South Florida as I am.  What we have to choose from is one candidate whose forced sexualization agenda is one of personal depravity and the other whose forced sexualization agenda is a matter of public policy.
  • Personally I’ve always gravitated to the “remnant” mentality.  I was raised listening to the encounter with the rich young ruler and the parable of the rich man and Lazarus; somehow anything else misses the point.  The most active alternative along these lines is the “Benedict Option” advocated by Rod Dreher.  Maintaining that in a totalitarian society–even one with periodic elections–won’t be easy.

Buoyancy and Stability: An Introduction

Ever since people set out to sea in ships, the issues of buoyancy and stability have been of importance. In spite of this, the treatment it receives in textbooks is often lacking. Following is an overview of the subject; basic understanding of the principles is essential in performing the experiment and interpreting the results.


Buoyancy is ultimately what makes things float, such as the buoy in Figure 1. This is true whether the material the boat is made of is lighter than water (like the balsa wood rafts Thor Heyerdahl and his crew crossed the Pacific with in 1947) or heavier than water. The latter would include objects from the buoy shown to the ships of the U.S. Navy.

Figure 1
Figure 1

The basic concept is very simple: for anything placed in a fluid medium, the upward force the medium exerts on the body is equal to the weight of the fluid the body displaces. This is not only true of bodies placed in water; it is also true of those in air. The difference is that, for those in air, the weight of the air displaced is usually not enough to “float” the aircraft. A notable exception are dirigibles such as the “Goodyear blimp,” which is filled with helium, a gas lighter than air. Another lighter-than-air gas used is hydrogen. This is very combustible, as everyone was reminded of when the Hindenburg caught fire in New Jersey in 1938.

Most buoyancy applications are marine ones, and it is those we will concentrate on in this experiment. We will also concentrate on rectangular forms and flat-bottomed vessels, which simplifies the math somewhat. However, these principles can be extended to just about any floating craft.

Using a flat-bottomed craft also makes it easier to understand why displacing a fluid works. Consider first the following: how the force of the fluid on the flat hull of a craft varies with depth1:

Figure 2: Illustrating Water Pressure Increasing in Proportion to Draught

For a fluid at rest, the hydrostatic pressure increases linearly with depth, thus


Figure 3 Inadequate Freeboard
Figure 3 Inadequate Freeboard

where p is the hydrostatic pressure, γ is the unit weight of the water, and D is the depth from the water’s surface to the bottommost point of the vessel, usually called the draught. This distance from the water line to the top of the rectangle (the gunwale) is called the freeboard; the results of inadequate freeboard can be seen in Figure 3.

In any case, for a vessel of beam (width) W and a length L the volume it displaces is given by the equation


Combining and rearranging these two equations,


For the boat to float, it has to be in static equilibrium, and so the downward force of the weight of the boat Wboat must equal the upward force Fbuoyant. Therefore,


So we’ve established a relationship between the weight of the boat and the volume of water it displaces. The “far right” hand side only applies to boats with a flat bottom and straight sides.

What this means is that there are three ways we can weigh an existing boat:

  1. We can simply weigh it on a scale. For small boats this isn’t too difficult; larger ones can be tricky.  We can then estimate how far it will sink into the water.

  2. We can measure the freeboard, then obtain D and, knowing L, W and the unit weight of water, we can compute the weight of the boat. This works easily for rectangular boats; for real boats, you have to determine the relationship between the actual waterline and the displacement, then see where the actual waterline ends up.

  3. We can use an overflow method, which is okay for small experiments (like Archimedes used) but not so hot on a larger scale.  But this illustrates our concept.

Procedure for determining volume of water displacement2:

Figure 4 Displacement


Buoyancy is a fairly straightforward concept, although it may be a little hard to grasp up front. Stability—the ability of the ship to resist overturning—is a little more difficult, although it’s obviously important, as the following diagram of a ship with waves coming at the beam shows3.

Figure 5: Showing the Transverse Movements of an Easy-Rolling Vessel Among Waves, and Also of a Raft

Let’s define (or recall) a couple of terms.

Centre of Gravity: this is easy, mathematically this is the centroid of the mass or weight of the ship. An illustration of this is below.

Figure 6: Centre of Gravity of a Ship

Centre of Buoyancy: this is a little trickier, this is the centroid of the cross-sectional area of the ship under the water line, as shown below.

Figure 7: Centre of Buoyancy of a Box-Shaped Vessel

As you can see, for a box-shaped vessel which is not listing (i.e., leaning at an angle) or has no squat (i.e., not angled along the length of the boat) the centre of buoyancy is located halfway down the draught of the vessel, halfway across the beam, and dead amidships.

The centre of gravity and the centre of buoyancy are not necessarily at the same place; in fact, they are usually different. That difference determines both the stability of the ship and, literally, how it rolls.

We know that motor vehicles with high centres of gravity (such as off-road vehicles) are more prone to turn over in use than those with lower centres of gravity. Ships are the same; we need to have a way to decide how stable a ship is and whether there is a point that a ship becomes unconditionally stable or unconditionally unstable.

As long as a ship is upright, and both the centre of gravity and the centre of buoyancy are in the centre of the ship in all respects, it is theoretically possible for a ship never to turn over. As a practical matter this is impossible; even very large ships like cruise ships, which use their size to resist roll in most wave situations, are going to roll some. Below is a diagram which shows the centre of gravity and the centre of buoyancy for a ship which is upright and which is inclined 14º.

Figure 8: Vessel Floating Upright, and Inclined 14 Degrees

We need to look at this carefully and note the following:

  • The point G is the centre of gravity of the ship.

  • The point B or B’ is the centre of buoyancy of the ship. In the course of inclination the centre of buoyancy will change because the shape of the cross-section under the waterline changes; this is fairly simple to calculate for rectangular ships and more complicated for curved hull shapes.

  • The point M is the metastatic point of the ship. The distance GM is called the metastatic height of the ship.

  • If point G is below point B or B’, the ship is unconditionally stable; it will not turn over unless G and B’ is changed by taking on water, shifting cargo in the ship, etc.

  • If point G is below point M, the ship is conditionally stable, and if point G is above point M, the ship is unconditionally unstable.

The reason for this last point is simple: the ship above is rolling in a clockwise direction. The resisting moment of the buoyancy, calculated by (GZ)(Wbuoyant) is counter-clockwise, as the buoyant force is upward. This is true as long as G is below M. If G moves upward above M, then the now driving moment (GZ)(Wbuoyant) turns clockwise, the same direction as the rolling of the ship, and the ship will generally turn over4.

Thus the location of M, abstract as it may seem, becomes a critical part of the design of a ship. But how is it done? There are two methods we will discuss here of determining the metastatic height of a ship.

Determining Metastatic Height

Theoretical Method

This method uses the following formula to determine the location of the metacentre:


For a rectangular vessel, the moment of inertia is the same as we used in mechanics of materials, i.e., LW3/12, and is applied as follows:

The displacement volume was given earlier. We then compute the distance between the metacentre M and the centre of buoyancy B as follows:

Note carefully that this is NOT the metacentric height GM; it is then necessary to subtract the distance from the centre of buoyancy to the centre of gravity from this result to obtain GM. This is done as follows:

Figure 9: Computing GM From the Height of the Metacentre Above the Centre of Buoyancy

It’s worth noting here that the location of point M is independent of the centre of gravity and dependent upon the geometry of the ship and its volume under the water line (or total weight.)

Timing the Roll

This method is sort of an “old salt’s” rule of thumb method. First, let’s define the roll time. The roll time is the time it takes for a ship to start from rest at an angle of roll (port or starboard,) roll to the opposite side, and return to the original orientation. This can be approximated by the equation5


where tr = roll time of ship, seconds
GM = metastatic height of ship, meters or feet
W = beam of ship, meters or feet
C = constant based on units of GM and B
= 0.44 for units of feet
= 0.80 for units of meters

Solving for metastatic height,


This is significant for another reason: another rule of thumb used in yacht design is that the roll time is seconds should be between 1 and 1.1 times the beam W of the boat in meters6. <