## Vulcan Hammers and the Gates Formula

For many years, Vulcan included Engineering News Formula charts and data in its literature.  Vulcan dropped the EN formula out of its literature in the 1970’s, for two reasons: the wave equation was in the ascendancy, and endorsement of the EN formula was an implied endorsement of the “bearing power” of the piles they drove, an endorsement which Vulcan was justifiably reluctant to make.

Nevertheless, the use of dynamic formulae persists for smaller projects and is embedded in many specifications.  For this purpose, the FHWA favours the Modified Gates Formula, and this is discussed in the latest edition of their Design and Construction of Driven Pile Foundations.  The section on the Modified Gates Formula is reproduced below:

Gates Formula tables can be found for many Vulcan hammers can be found at the Vulcan Foundation website.

Copies of the FHWA Design and Construction of Driven Pile Foundations can be obtained by clicking on the cover images to the right.

## Vulcan #1 Hammer in Ohio

Below are three photos taken of a Vulcan #1 hammer in Mentor, Ohio.  It’s in fixed leaders with a moonbeam-style spotter.  The hammer was made in Chicago, which means that it’s probably older than sixty years.  Thanks to Ken Foster for sharing these great photos.

## Compressible Flow Through Nozzles, and the Vulcan 06 Valve

Most of our fluid mechanics offerings are on our companion site, Chet Aero Marine.  This topic, and the way we plan to treat it, is so intertwined with the history of Vulcan’s product line that we’re posting it here.  Hopefully it will be useful in understanding both.  It’s a offshoot of Vulcan’s valve loss study in the late 1970’s and early 1980’s, and it led to an important decision in that effort.  I am indebted to Bob Daniel at Georgia Tech for this presentation.

## Basics of Compressible Flow Through Nozzles and Other Orifices

The basics of incompressible flow through nozzles, and the losses that take place, is discussed here in detail.  The first complicating factor when adding compressibility is the density change in the fluid.  For this study we will consider only ideal gases.

Consider a simple orifice configuration such as is shown below.

The mass flow through this system for an ideal gas is given by the equation

$\dot{ m }=A'_{{o}}\rho_{{1}}\left ({\frac {p_{{2}}}{p_{{1}}}}\right )^{{k}^{-1}}\sqrt {2}\sqrt {g_{{c}}kRT_{{1}}\left (1-\left ({\frac {p_{{2}}}{p_{{1}}}}\right )^{{\frac {k-1}{k}}}\right )\left (k-1\right )^{-1}}{\frac {1}{\sqrt {1-{A_{{o}}}^{2}\left ({\frac {p_{{2}}}{p_{{1}}}}\right )^{2\,{k}^{-1}}{A_{{1}}}^{-2}}}}$

where

• $\dot{m} =$ mass flow rate, $\frac{lb_m}{sec}$
• $A_o =$ throat area of orifice, $ft^2$
• $A'_o =$ adjusted throat area of orifice (see below,) $ft^2$
• $\rho_1 =$ upstream density, $\frac{lb_m}{ft^3}$
• $p_1 =$ upstream pressure, psfa
• $p_2 =$ downstream pressure, psfa
• $g_c =$ gravitational constant $= 32.2 \frac{lb_m-ft}{lb_f-sec^2}$
• $k =$ ideal gas constant or ratio of specific heats $= 1.4$ for air
• $R =$ gas constant $= 53.35 \frac{ft-lb_f}{lb_m\,^\circ R}$
• $T_1 =$ upstream absolute temperature $\,^\circ R$

At this point we need to state two modifications for this equation.

First, we need to eliminate the density, which we can do using the ideal gas equation

$\rho_1 = {\frac {p_{{1}}}{RT_{{1}}}}$

Second, we should like to convert the mass flow rate into the equivalent volumetric flow rate for free air.  Most air compressors (and our goal is to determine the size of an air compressor needed to run a test through this valve) are rated in volumetric flow of free air in cubic feet per minute (SCFM.)  This is also the basis for the air consumption ratings for Vulcan hammers as well, both adiabatic and isothermal.  This is accomplished by using the equation

$\dot{m} = {\frac {1}{60}}\,{\it SCFM}\,\rho_{{{\it std}}}$

Making these substitutions (with a little algebra) yields

$SCFM = 60\,A'_{{o}}p_{{1}}\left ({\frac {p_{{2}}}{p_{{1}}}}\right )^{{k}^{-1}}\sqrt {2}\sqrt {-g_{{c}}kRT_{{1}}\left (-1+\left ({\frac {p_{{2}}}{p_{{1}}}}\right )^{{\frac{k-1}{k}}}\right )\left (k-1\right )^{-1}}{\rho_{{{\it std}}}}^{-1}{R}^{-1}{T_{{1}}}^{-1}{\frac {1}{\sqrt {-\left(-{A_{{1}}}^{2}+{A_{{o}}}^{2}\left ({\frac {p_{{2}}}{p_{{1}}}}\right )^{2 \,{k}^{-1}}\right){A_{{1}}}^{-2}}}}$

In this article the coefficient of discharge $C_D$ is discussed.  It is also the ratio of the effective throat area to the total throat area, or

$A'_o = C_DA_o$

We are basically considering the energy losses due to friction as an additional geometric constriction in the system.

One final–and very important–restriction on these equations is the critical pressure, given by the equation

$p_c =p_{{1}}\left (2\,\left (k+1\right )^{-1}\right )^{{\frac {k}{k-1}}}$

The critical pressure is the downstream pressure for a given upstream pressure below which the flow is “choked,” i.e., the mass or volumetric flow rate will not increase no matter how much you either increase the upstream pressure or decrease the downstream pressure.  This limitation, which was observed by Saint-Venant, is due to achieving the velocity of sound with the flow through the nozzle or valve.  A more common way of expressing this is to consider the critical pressure ratio, or

$p_{cr} = \frac{p_c}{p_{{1}}} = \left (2\,\left (k+1\right )^{-1}\right )^{{\frac {k}{k-1}}}$

As you can see, this is strictly a function of the ideal gas constant.  It’s certainly possible to get around this using a converging-diverging nozzle, but most nozzles, valves or orifices are not like this, and certainly not a Vulcan 06 valve.  We now turn to the analysis of this valve as an example of these calculations.

## Application: the Vulcan 06 Valve

The first thing we should note is that pile driving equipment (except that which is used underwater) is designed to operate at sea level.  Using this calculator and the standard day, free air has the following properties:

• Temperature: 518.67 °R
• Density: $\rho_{std} = 0.00237 \frac{slugs}{ft^3} = 0.0763 \frac{lb_m}{ft^3}$
• Pressure: $2116.22 \frac{lb}{ft^2}$ (or psfa)

Now let’s consider the valve for the 06 hammer (which is identical to the #1 hammer.)  A valve setting diagram (with basic flow lines to show the flow) is shown below.

Note the references to steam.  Until before World War II most of these hammers (along with most construction equipment) was run on steam.  With its highly variable gas constant and ability to condense back to liquid, steam presented significant analysis challenges for the designers of heavy equipment during the last part of the nineteenth century and the early part of the twentieth.  For our purposes we’ll stick with air.

There are two cases of interest:

• The left panel shows the air entering the hammer and passing through the valve to the cylinder.  Pressurising the cylinder induces upward pressure on the piston and raises the ram.  The valve position (which shows the inlet port barely cracked) is shown for setting purposes; in operation the valve was rotated more anti-clockwise, opening the inlet port.
• The centre panel shows exhaust,  where air is allowed to escape from the cylinder.  The piston is no longer pressurised and the ram falls to impact.

According to the vulcanhammer.info Guide to Pile Driving Equipment, the rated operating pressure for the Vulcan 06 at the hammer is 100 psig = 14,400 psfg = 16,516.22 psfa = 114.7 psia.  For simplicity’s sake, we can consider the two cases as mirror images of each other.  In other words, the upstream pressure in both cases is the rated operating pressure.  This should certainly be the case during air admission into the hammer.  For the exhaust, it should be true at the beginning of exhaust.  Conversely, at the beginning of intake the downstream pressure should be atmospheric (or nearly so) and always so for exhaust.

From this and the physical characteristics of the system, we can state the following properties:

• Upstream pressure = 114.7 psia
• Downstream pressure = 14.7 psia
• Upstream area (from hammer geometry, approximate) $A_1 = 0.00705 ft^2$
• Throat area $A_o = 0.00407 ft^2$
• Coefficient of Discharge, assuming sharp-edge orifice conditions $C_D = 0.6$
• Adjusted throat area $A'_o = 0.00407 \times 0.6 = 0.002442 ft^2$

At this point calculating the flow in the valve should be a straightforward application of the flow equations, but there is one complicating factor: choked flow, which is predicted using the critical pressure ratio.  For the case where $k = 1.4$, the critical pressure ratio $p_{cr} = .528$.  Obviously the ratio of the upstream pressure and the downstream pressure is greater than that.  There are two ways of considering this problem.

The first is to fix the downstream pressure and then compute the upstream pressure with the maximum flow.  In this case $p_1 = \frac{p_{atm}}{p_{cr}} =$ 27.84 psia = 13.14 psig.  This isn’t very high; it means that it doesn’t take much pressure feeding into the atmosphere to induce critical flow.  It is why, for example, during the “crack of the exhaust,” the flow starts out as constant and then shortly begins to dissipate.  The smaller the orifice, the longer the time to “blow down” the interior of the hammer or to fill the cylinder with pressurised air.

The reverse is to fix the upstream pressure and then to vary the downstream pressure.  The critical downstream pressure is now $p_2 = p_1 \times p_{cr} = 114.7 \times 0.528 =$ 60.59 psia = 45.89 psig.  This means that, when the cylinder is pressurising at the beginning of the upstroke, the cylinder pressure needs to rise to the critical pressure before the flow rate begins to decrease.

We will concentrate on the latter case.  If we substitute everything except the downstream pressure (expressed in psia,) we have

$SCFM = 0.05464605129\,{\frac {{{\it p_2}}^{ 0.7142857143}\sqrt { 3126523.400-806519.7237\,{{\it p_2}}^{ 0.2857142857}}}{\sqrt { 0.9999999996-0.0003806949619\,{{\it p_2}}^{ 1.428571429}}}}$

If $p_2$ falls below the critical pressure, the flow is unaffected by the further drop and is constant. In this case the critical flow is 795 CFM.  For downstream pressures above the critical pressure, the flow varies as shown below.

As noted earlier, when air is first admitted into the cylinder the flow is constant.  Once the critical pressure ratio is passed, the flow drops until the two pressures are equal.

It was this large volume of flow which prevented the use of the 06 valve (which could have been separated from the cylinder using a valve liner) in the valve loss study.  The smaller DGH-100 valve was used instead.

It is interesting to note that the rated air consumption of the hammer is 625 cfm.  This is lower than the instantaneous critical flow.   Although on the surface it seems inevitable that the hammer will “outrun” the compressor, as a further complication the hammer does not receive air on a continuous basis but on an intermittent one.  For much of the stroke the compressor is “dead headed” and no air is admitted into the cylinder from the compressor.  To properly operate such a device, a large receiver tank is needed to provide the flow when it is needed.  The lack of such large tanks on modern compressors is a major challenge to the proper operation of air pile hammers.

## The Best Way to Celebrate Your 120th Birthday is With a New Slide Bar Part

On our Engineering at Vulcan page, we posted this general arrangement of the Vulcan #2 dated 1887.

Little did we suspect that we’d need that drawing, but then these photos from Crofton Diving of Portsmouth, VA, arrived:

The hammer in question is Vulcan S/N 116, originally sold to the Florida East Coat Railroad (not far from the West Palm Beach facility) in 1897.  The distinctive “open” slide bar design was changed about that time to what is on virtually every Warrington-Vulcan and Super-Vulcan hammer made since.  Vulcan Foundation Equipment  was able to make the spare parts Crofton required from the original detail drawings.

“Planned obsolescence” wasn’t the Vulcan way in 1897 or afterwards, which is why a 120-year old product is still driving pile and being useful to the contractor.

## ZWAVE

ZWAVE was Vulcan’s foray into the wave equation program field. It was an outgrowth of research that dated back to the late 1970’s on the magnitude of impact forces of its hammers on pile tops, so as to estimate both the loads on the equipment and the stresses on the piles. The first tangible result of this was a method and computer program based on numerical methods applied to semi-infinite pile theory; this was presented at the Offshore Technology Conference in 1987.

It became clear, however, that such a solution would not be as comprehensive as necessary, so ZWAVE was developed. Developed for MS-DOS computers, it’s “Preliminary Trial Release” (beta version) was released in 1987. The two proper releases (1.0 and 1.1) were done in 1988, after which time there was some work done the program but it had no further releases.  (The user’s manual for 1.0 can be downloaded here.)

Also in 1988 was the paper describing the program, “A New Type of Wave Equation Analysis Program,” presented at the Third International Conference on the Application of Stress-Wave Theory to Piles in Ottawa, Ontario, in May 1988. This paper is available in PDF format and can be downloaded by clicking the link below.

Unfortunately ZWAVE’s copyright status makes it impossible to make the program available for download. The paper, however, shows many of the advanced features of the program which were both referenced by later authors and included in later wave equation programs.

### Abstract for “A New Type of Wave Equation Analysis Program”

This paper describes a new wave equation analysis program called ZWAVE, which is a program specifically for external combustion hammers. The program is described in detail, the discussion dealing with topics concerning the program such as 1) the numerical method the program uses to integrate the wave equation, which is different from most other wave equation programs; 2) the modelling process of both cushioned and cushionless hammers; 3) the automated generation of mass and spring values for both hammer and pile; 4) the method of dealing with plastic cushions; 5) the use of a recently developed model for computing shaft resistance during driving; 6) the computation and generation of values based on basic soil properties such as shear modulus, Poisson’s Ratio and soil density; 7) the completely interactive method of feeding data to the program; 8) the method used to compute the anticipated rebound and the energy used to plastically deform the soil; and 9) the format of the interactive input of the program and the program’s output. Sample problems for the program, along with comparison of the program results with data gathered in the field, are presented.

## Vulcan Vibratory Hammers and Vibratory Technology

By World War II, Vulcan’s air/steam hammer line dominated its production and revenue stream. Of all of the attempts Vulcan made to diversify is pile hammer line after that time, probably the most successful was its line of vibratory pile hammers.

Vibratory pile driving equipment represented a major departure for Vulcan, but it also represents an interesting technology in its own right. In addition to recounting Vulcan’s experience, we have a wide variety of items on vibratory technology in general:

Need a field service manual for your Vulcan vibratory hammer? Or other information. Much of that is contained in the Vulcanhammer.info Guide to Pile Driving Equipment, information about which is here.

## Vulcan High-Frequency Vibratory Hammers

The mid-1980’s were lean years at Vulcan. The offshore market was still down, the aftermath of the collapse of oil prices earlier in the decade. Vulcan’s own diesel program had to be stopped, plagued by design and manufacturing problems and an overvalued US Dollar. The vibratory hammer program was going reasonably well but the market was competitive. Vulcan had reached the point where it had effectively closed its own manufacturing facility and farmed out what was left.

It was in this gloomy situation that Vulcan designed and produced one of the most innovative products it had ever produced, the 400 vibratory hammer, the first of Vulcan’s high-frequency machines.

High frequency (~2400 RPM, not to be confused with the ~7200 RPM resonant machines) vibratory drivers had been produced in Europe. Depending upon the soil conditions and configuration of the pile, the vibrations used to drive or extract the pile can also be transmitted to neighbouring structures. Since European contractors drove piles more frequently in close quarters with sensitive structures than their American counterparts, European vibratory manufacturers produced high frequency machines first. Their higher frequency, combined with lower amplitude for the dynamic force, reduce the transmitted vibrations through most soils.

Vulcan’s rationale for a high frequency machine, however, was somewhat different. The first impetus for the 400 was the development of aluminium sheet piling, which made development of a driver smaller than the 1150 attractive. MKT had already developed a medium-frequency small machine (the V-2) to drive aluminium sheet piling, but the machine a) weighed over a US ton and b) had a clamp suited to steel piling, which mangled the heads of aluminium sheets.

What was needed was a lighter machine whose clamp was easier on the pile. Vulcan’s interpretation of the theoretical data led it to believe that a high frequency machine would drive the piles (which was certainly the case with the lighter sheeting sections.) The result was the first 400 vibratory hammer, designed and built in the summer of 1987.

The 400 had several innovative features:

• A one piece gear-eccentric, machined out of plate with the eccentric weight burned out. The gear teeth were a much smaller pitch than their medium frequency counterparts, a feature replicated on the “A” series machines four years later. The small pitch ran more quietly an dispensed with the need for surface hardening.
• A clamp that was burned out of plate. The cylinder bolted to it used the flat end of the rod as the movable jaw. This only left a shallow round dent in the sheeting when clamped.
• The “U” configuration which wrapped around the exciter case and transmitted the force from the crane to the pile during extraction. This and other features were subject to U.S. Patent 4,819,740. (This patent has been a nuisance to Vulcan’s competitors for long time, cited in several patents from inventors at HPSI, APE, J&M, ICE and MGF.)
• It was the first Vulcan pile driving machine to completely dispense with castings.

The result was a machine that weighed only 1100 lbs.–half of the MKT V-2–and still drove the piles successfully.

## Vulcan’s Medium Frequency Vibratory Hammers

In 1984 Vulcan re-entered the vibratory hammer market with the introduction of the 1150 vibratory hammer. This hammer made its debut on a project in Bangor, Maine for Cianbro Construction. More suited for the American market and adequately powered, these machines were far more successful than the Vulcor hammers had been.

The technology used was pretty typical for vibratory hammers of the era, including the large-pitch teeth gears bolted to cast steel eccentrics, 355 mm (14″) throat width for American-style sheeting installation, Volvo hydraulic piston motors (for the high pressure units; vane style motors were used on the low pressure 1150,) and a clamp with an industrial style cylinder bolted on to push the movable jaw into the fixed jaw. Both jaws had two parallel sets of teeth with a gap in between to accommodate the interlocks on the sheet piles, which enabled the hammer to drive two sheets at a time.

Vulcan produced three sizes of medium frequency hammers, the 1150, 2300 and 4600. The size designated the eccentric moment of the hammer in inch-pounds. All of the hammers rotated at 1600 RPM.

Vulcan used the HPSI power pack for its vibratory hammer throughout the 1980’s. (One of these is shown on the flatbed trailer in the 4600 photo below.) This power pack was simple and reliable, using air controls (as opposed to the electric controls used by competitors such as ICE and later APE.

Note: if you’re looking for service and other technical information on Vulcan vibratory hammers, take a look at the Vulcanhammer.info Guide to Pile Driving Equipment.

Below: a 2300 on the job driving h-beams in Portsmouth, Virginia, in 1990. The contractor was Tidewater Construction. A diesel hammer can be heard driving piles in the background for part of the video.

Below: the 2300L extracting soldier beams in Atlanta, Georgia, in December 1990. The fact that these machines can both drive and extract piling without modification is part of their appeal.

Below: a video of the installation of bearings in the 2300L, and a little “tour” of PACO’s yard.

### The “A” Series Vibratories

In 1991 Vulcan introduced the “A” series of hammers (1150A, 2300A and 4600A) series of hammers. The biggest changes were a) the abandonment of the Morse shear fenders and b) the complete reconfiguration of the gear and eccentric design, inspired by information obtained from the Soviets. The first “A” series hammer was a 2300A, first used on a job by Agate Construction in New Jersey.

Vulcan also began to manufacture its own power packs, where it was able to make many technological advances.

### Foster Units

One of Vulcan’s more interesting ventures in the 1990’s was the private label manufacture of a line of vibratory hammers for L.B. Foster in Pittsburgh. The first hammer to be produced was a replica of Foster’s existing 1800 unit, but it became apparent that this unit was very expensive to produce. Vulcan then designed a line of medium frequency vibratory hammers, the 1050, 2100 and 4200 hammers. With the combination of Vulcan’s and Foster’s experience in vibratory hammer design and manufacture, this was the best line of medium-frequency vibratory hammers that Vulcan ever produced.

Some general arrangements of the Foster hammers are here.

### After the Acquisition

After it was acquired by Cari Capital, the company continued to support the line; however, it was left behind when Vulcan Foundation Equipment acquired the air/steam hammer line in 2001. It was ultimately sold at auction the following year.  Current service and support for these units is furnished by Pile Hammer Equipment.

## Uraga/Vulcor Vibratory Hammer

Vulcan’s first venture into the vibratory market took place in the 1960’s with the introduction of the Uraga electric vibratory hammer from Japan, which Vulcan marketed as the Vulcor Vibratory Hammer.

Vibratory pile driving technology had been developed in the Soviet Union. One of the first countries to pick up the technology was Japan. With its volcanic soils, it is an ideal place for a vibratory hammer to be used.

Most early Japanese vibratory hammers (which are described some here) followed the Soviet pattern of electric motor(s) driving eccentrics through a chain drive system. (An example of this kind of design is shown here.) This unimaginative application of the technology prompted one Soviet trade official to describe the Japanese as “not very good students.”

The Uraga/Vulcor machine was a departure in that Uraga reversed the rotor and stator on the electric motors and positioned one motor inside of each eccentric. This resulted in a vibrator with a more direct drive than has been seen before or since, making for an efficient construction and operation.

Unfortunately the width of the machine clashed with the normal American practice of setting the sheets before driving, which requires either that the vibratory hammer be narrow enough (less than 355 mm) at the throat or use an extension (which adds to both the vibrating mass and hanging weight of the hammer.) Some Uraga machines also suffered from misalignment of the eccentric bearings, a function in part of the “modular” construction of the machines (to increase the number of eccentrics, it was simply necessary to add another “stack” to the unit.

All of these difficuties, combined with American contractors’ aversion to electrics on the job, put the Vulcor at a disdavantage to other vibratories coming into the U.S. By the time Vulcan moved to West Palm Beach, the Vulcor programme was pretty much over and it would be another twenty years before Vulcan would attempt a vibratory hammer again.

More on the Uraga/Vulcor Hammer:

## Vulcan Diesel Hammers

At one point or another in its history, Vulcan attempted to produce or market every type of pile driver made. Probably the persistently least successful type were the diesel hammers. Vulcan’s failure to manufacture and/or market a widely accepted diesel hammer was a significant long-term problem for the company.

Nevertheless diesel hammers are an important and interesting type of impact pile driver. This section of vulcanhammer.info discusses diesel hammers in general and Vulcan’s several attempts to enter the market.