Powder Chambers, Some Weird, Some Regular, TO BE TESTED-See Photos

[seacoastartillery]

The Effect of various Chamber Shapes upon Efficiency of Powder Burn
Proved by
Distances which Like Weight Projectiles are Thrown

    We simply would like to determine by actual experiment, which form of cannon chamber of several  is most efficient at burning a measured charge of BP proved by it’s projection of a standard weight projectile the longest distance.  Over the years Mike and I have seen here and there various pronouncements  on which chamber shape is best, based on the distance of shot projection.  All of these “experts” issued their sage conclusions based on theory alone, with no attendant empirical evidence with a tabulation of the results of experimentation.  We would like to fill that “Observation of Experiment” gap.

     The most efficient chamber shape based on the number of mentions is the Spherical which may indeed produce the greatest distance of projection.  It’s not likely to be the artilleryman’s favorite though.  Look at that shape; can you imagine how difficult it would be to clean THAT?

     We would like to build inserts, each having a different chamber shape, which could be dropped into a common tube with a slip fit and be mechanically locked into place by a robust vent liner tube.  Probably a mortar would be easiest to work with while conducting these experiments.

     The data gathered would answer several important questions such as which chamber shape is Most Efficient, which is Easiest to Produce and which is Best when you consider efficiency of powder burn, ease of manufacture AND acceptability to muzzle loading artillerymen as far as loading and cleaning is concerned.

       The following came from Craig Swaine’s excellent artillery blog called “To the Sound of the Guns” and goes to prove that the well known designers studied this area of design and had definite opinions about which chamber shape provided advantages. “Rodman also took the time to determine, based on his compiled data, the best profile for the gun’s chamber (or bore bottom as he called it).  The preceding experiments indicated the traditional flat-bottomed bore tended to crack at the corners.  In the course of experiments Rodman found the sub-caliber chambers of the old Columbiads detrimental to performance.  He wrote, “There should be no angles, either salient or re-entrant, in the termination of the bore, but the surfaces of the bore and of its termination should be tangent along their lines of junction…. the semi-ellipsoid is believed to be the best and true termination.” However, the casting plan diagram showed that of a hemisphere.” 

      For those of you still interested in our planned “Blast Effect” Mortar Experiments, please don’t worry; those are planned to be started as soon as we get back from our seacoast cannon delivery trip in late September.  The construction of those mortars will most likely start in the fourth week of September and the Chamber Shape mortar build right after those are complete.  The 1” Cannon Blanks will be developed concurrently with these sets of experiments and afterward.  Cannon Blank production should start in late December.

           Below are a few drawings, diagrams and a photo of the Chamber Shapes we will consider building for these experiments:

SUB-CALIBER   CYLINDRICAL      “In the first, the bottom of the bore at the mouth of the chamber is formed of a portion of a sphere, so that the projectile closes the mouth of the chamber. This is the chamber used in our different howitzers, and in the eprouvette mortar.  It is, however, joined to the bore in the way above described only in the eprouvette, and in one of the howitzers (the 8 -in. siege). In the other howitzers it is connected by means of a conical surface, the junctions being rounded off to prevent being worn away by the action of the powder.  Cylindrical chambers, when narrow and deep, give greater ranges than shallow wide ones, which do not confine the powder so much, but as in the former the gas acts on but a small segment of the projectile (usually hollow), it sometimes breaks it;  and, for this reason, too great a depth in cylindrical chambers is avoided.”    This is quoted from the  Artillerist’s Manual by Gibbon published in 1860. 





GOMER       “The Gomer chamber (after its inventor) consists of the frustrum of a cone connected with the bore by a portion of the surface of a sphere. This kind of chamber is considered the most advantageous for mortars, and is used in most of ours. Being large at the mouth, it allows the powder to act on an entire hemisphere of the projectile, and no risk is run of breaking it.  It, however, gives a less range than either of the others, but its capacity is greater.”   From the  Artillerist’s Manual.  This chamber was favored by Admiral Dahlgren for many of his naval guns including the widely used, IX-inch Dahlgren Shell Gun.



Spherical      Most of what we been able to find about this type comes from the technical journals of the late 1700s and early 1800s.  Iron, compiled by Percy Sholto and published by Knight and Lacy, London 1825 is a good source for further reading.  The three articles in that magazine for the metal working industry give us the most information about this chamber. Although this type of chamber is difficult to clean, all of our reading on this subject leads us to believe that the spherical form will be the most efficient chamber of the three.

   Qualities of the spherical form chamber are:  power, most dangerous and difficult to clean, (known to harbor embers), and difficult to manufacture.  Also one very important dimension is contained in them.  The short cylinder between the spherical chamber and the ball seat is, at optimum size, one-half the diameter of the powder chamber.




Hemispherical  This form of chamber had a full bore size powder area terminated by a hemisphere shape.This chamber type is typified by Parrott rifles of all sizes.Most Rodman guns had a similar chamber that was a slightly extended hemisphere.




  Flat Bottom    This chamber was typified by that used by Sir Wm Armstrong in his large muzzle loading rifles of the 1860s-1870s.  The photo is by Seacoast Artillery of the 150 Pdr. Armstrong Rifle at the United States Military Academy at West Point, New York.  We measured the bore termination with a special 12 foot long probe and found the bore end t o be flat and perpendicular to the bore axis with a 1” radius all around.  The Whitworth 80 Pdrs. used on Morris I. in Federal siege operations against Confederate held Ft. Sumter in 1863 both had this form chamber.  Naval crews were used to man the Whitworth rifles.







Ellipsoidal    This chamber is shaped like one half of a football. This ellipsoidal chamber  type is commonly found on Dahlgren Guns.  The final version of the XV-inch Naval Gun used a simplified lengthened hemispheroid chamber instead of the more difficult to produce ellipsoidal chamber. Remember that the final drawing for the 15-inch Rodman Gun also showed a hemispherical chamber bottom.




TEAT CHAMBER with ELBOW VENT              This unique chamber is the invention of Admiral Dahlgren and is certainly the most controversial of all.  The design had many critics, not the least of whom, were the machinists who were charged with the task of producing it with it’s almost impossible to produce, elbow vent.

  The Big Guns  by Olmstead, Stark and Tucker has the best section of information on this unusual design.  “Dahlgren’s astounding advocacy of elbow vents remains unclear.  His widow abstracted notes of Feb. 1862 from his diary, unfortunately more meaningful to the author than to anyone else.  They imply Dahlgren’s conviction that weapon strength and endurance will improve if the vent is directed rearward along the axis behind the chamber of a gun.  After an inch or so, such a vent turns a sharp right angle.  Doing so requires two .200-inch holes to intersect, the longer of which may range from 16 to 32 inches long.  We find no record and cannot imagine how Dahlgren proposed always to assure a precise meet of both holes, or how to clear both with a vent punch.  A machinist’s rule of thumb for accurate drilling is to limit hole depth to 20 times its diameter.  Dahlgren’s elbow vents, however, proposed one .200-inch hole precisely to intersect another at distances from 80 to 160 diameters, a sobering prospect for any machinist.  Fort Pitt Foundry declined responsibility for drilling such vents, on one occasion returning a XX-inch drawing showing one.”

Here is a separate quote on the same subject:“Experiments in 1862 apparently convinced Dahlgren that a massive inserted copper bore bottom or a small extension toward the rear, either of them vented rearward from its center, would somehow improve cannon endurance.  A dozen years of experience with round bottom Gomer chambers and conventional vents should not have forced his surprising incorporation of the teat chamber with an elbow vent into his 6 April 1862 design for the first XV-inch.  A Navy department memorandum presented on 3 May 1864 before the Joint Committee on the Conduct of War included an anonymous opinion that the teat chamber “was not only the most inconvenient in service, but really hastened the rupture of the gun instead of preventing it.”  Earlier during the same hearings Charles Knap phrased himself more delicately, “I am persuaded that the chamber is mischievous.” 

          From  longer and more exhaustive concentration on Dahlgren than our own, Eugene B. Canfield generously shares a documented conclusion he intends to publish that no XV-inch gun was actually made with an elbow vent.” 




    If we have not mentioned a chamber shape that you know of,  please post it here.  We can build all of these mentioned which were in use by various nations from the 1500s to the 1800s.

  Although the Teat Chamber with the Elbow Vent is certainly the most interesting, please watch your language when commenting on this one as these GBO Forums are family oriented.  Thank you.  Any questions that you may have will be answered without delay. 

Tracy and Mike

[KABAR2]

So you have decided to make us work for it with micro-print......... hopefully everyone asking questions won't do the same......
Interesting topic you have my attention ........     

[Parrott-Cannon]

This will provide data to improve my interior ballistic model.  How ling before the data is available?

[seacoastartillery]

    KABAR2,     I thought I had gotten rid of all the miniature print before anyone could see it.  Guess not!  Glad you have some interest in these experiments.  We are finally getting to do something different which is what we love to do.


     Parrott-Cannon,   Hope the data does help you, we sure do appreciate all the wonderful work you have done on Artillery Ballistics.  It looks like we are two and a half to three months away from doing the BLAST EFFECT and then the Chamber Type Experiments.  It should take only two weeks for each set to be completed.

Thank you gentlemen for your interest,

Mike and Tracy

[keith44]

That spherical chamber should be approached with caution.  Early rifles firing black powder cartridges avoided sharply tapered or bottlenecked cartridges for many reasons.  Cleaning is not mentioned in anything I have read.

[KABAR2]

Where are you on your other testing? "operation Calliope" Or will this be part of it?

[seacoastartillery]

Keith,      We will be careful. After all what you pointed out is correct, because what you are doing with the Spherical is basically creating an exploding shell shaped chamber with a large size fuze well hole.  Because we like 4150 ordnance steel quite a lot and have a bunch of it from 5 Lb to 260 Lb. pieces, we will use that 30 Rc pre-hardened stock to make this shape and we will be conservative with the gas emergence hole, making it larger than the old technical journals called for.

KABAR2,     Here's a special reprint of paragraph 5 for you, because you are special and because Mike and I like visiting with you in Virginia Beach. 

      For those of you still interested in our planned “Blast Effect” Mortar Experiments, please don’t worry; those are planned to be started as soon as we get back from our seacoast cannon delivery trip in late September.  The construction of those mortars will most likely start in the fourth week of September and the Chamber Shape mortar build right after those are complete.  The 1” Cannon Blanks will be developed concurrently with these sets of experiments and afterward.  Cannon Blank production should start in late December.

That's it!

Tracy

[Victor3]

 I wanna inspect a sample of the spherical chamber in cross-section on a CMM to be sure you didn't cheat. 

[seacoastartillery]

      Frankly Victor neither Mike nor I would know how to cheat on this project or the Spheroid Chamber in particular.  When you are formally trained as a gunsmith as we both were at the Colorado School of Trades, any method and any material which yields a safe product is fair game.  So, if you are implying that creating a sphere shaped powder chamber out of two hemispheres is cheating, well, we don't see it that way.  On the other hand, I did a process work-up sheet on that method versus the drill and bore from solid method and found to my surprise that the drill and bore from solid won the time-on-task assessment by 47%, that is to mean that drilling and boring from a solid round of 4150 would take 47% less time than the creation of two hemispheres AND bolting them together with enough bolts to provide a redundant safety factor built into the design.  We figure that 9 bolts 3/8-16 size at 40 deg. Basic 9X should do it, but just think of how much time that would take for drilling DEEP holes, counterboring deep holes and tapping and deburring and assembly of all the parts.

     Simply put, we have drilled and bored hemisphere bore bottoms before, (our Mallets Mortar Jr. has one in 1.720" dia.), so why not just drill and bore the gas emergence hole out to full size down to the spherical chamber bottom, then starting at the radius dimension, probably 1.000", bore out a hemisphere toward the bottom with our favorite lathe boring bar tool, finishing with a 1/2" straight ahead radius tool to get the last little bit and then cut a reverse 1.000" radius upper hemisphere from the same starting point, but drawing the tool out of the hole by .005" each time.  No finishing tool switch is necessary, because the gas emergence hole is there.  The ball seat portion can be cut with the same boring bar as the chamber bottom tool, but to a different sheet of numbers because of the larger radius.

      Now if you are talking about complete deception by having a simple deep cylinder instead of a sphere shape, well if you really are thinking along those lines, then I guess you can't tell how excited we are about taking a year off from making the collector and museum stuff and doing really different, free lance things for a change.  Remember its been a solid 42 years of production work for us, with only one week breaks twice a year, so we deserve to cut loose and have a little fun and we are going to do just that!!

Tracy

[Cannon Cocker]

Leave it to Seacoastartillery to use the scientific method to intelligently discuss powder chambers.  I'm all appreciative eyes and ears. 

Here are a couple unique chambers from John Muller's book.

[Cannon Cocker]

Here's the other one.  It didn't show up.

[keith44]

to me it looks like the first one is causing an unwanted bore constriction and would increase pressures in the powder chamber.  The second one looks like what would have been something in the evolution and development process of the "gomer" chamber.

[seacoastartillery]

     Cannon Cocker,   Thanks so much for posting those two drawings from Muller's classic book on artillery.  We also appreciate the kind comment on intelligent discussion on powder chambers.  We certainly hope it goes that way!  Mike and I like the Concave Chamber drawing a lot more than the other, but not for the reasons most of you suspect.  We like the Concave Chamber, because it is unique and was most likely designed to increase powder gas pressure and cause a probable increase in projectile distance.  We will be making one of the Concave Chambers for sure, for the purpose of comparison to the Spherical Chamber.  It should be interesting to see which one burns it's powder more efficiently, propelling the standard weight projectile a greater distance.  We don't like the "Gomer, sort of" chamber because it's powder chamber violates a basic machined feature design rule which is:  Avoid specifying tapered voids less than 15 degrees included angle if possible as tool jamming and breakage could occur.  Tapers on collets and drill tapers are less than 15 degrees total so they will lock when you put them together.

     Keith,   We think the Concave Chamber designer wanted a bore constriction to purposely cause increased pressure for increased performance, but we merely think this is logical and do not have any documented proof of this opinion.  We sure do believe you are spot on regarding the evolution of the Gomer Chamber.  We could be more sure if we knew that date that the Gomer Chamber was first created and the date of the posted drawing.  That one does have a taper, although not much of one.  We don't like the cylindrical transition between the chamber and the ball seat either represented by the extra set of hidden (dashed) lines.  Sometimes. perhaps most often, weapons are designed haltingly, in fits and with stoppages caused by bad experimental results or lack of government funding.  This drawing, even for that period, does not have the look of a "finished" design.  That's our opinion based on looking over thousands of drawings from around the world over a 36 year period.

Thanks guys; you have advanced this discussion admirably.

Mike and Tracy


The Gomer in development chamber.




The Concave Chamber.

[keith44]

so you are thinking that the concave chamber might have had the intent of increasing the velocity of the gasses and possibly increasing the range of the mortar.  Clever if that is what the original designer had in mind.

[Victor3]

 Tracy,
 
 All I was trying to imply is that it's somewhat difficult to accurately machine a spherical section (as in the pic you show) down into the bottom of a fairly deep bore on a conventional lathe. Nothing more.
 
 But hey, I'm still just learning about this machining stuff, even ~40 years after I made my 1st chip. 

[seacoastartillery]

     Keith,   We think there must have been some real reason for designing the Concave Chamber, otherwise why cause the machinists of that day to hate your guts?  With no documents to prove it, increased pressure with a probable increase in range, is just a SWAG, but if you look carefully at it, you can see elements of longer Cylindrical Chambers and elements of the Spherical Chamber in this Concave or Truncated Ellipsoid Chamber, both of which caused increased pressure and range to result.  I just figured out the math for the Concave Chamber with it's truncation and I'm not afraid to admit that it took me quite a while, especially as I had to reduce the volume of a full ellipsoid by the amount of the elliptical cone portion which, of course, does not actually exist, except in theory, but must be removed from the full ellipsoid, so the volume is derived from only the void that actually exists.  Had to go to a Nasa nose cone volume calc. site to get it.  Another reason it took so long was the fact that I'm trying to make all of these different chambers hold exactly 4 cubic inches of BP.  That volume just seemed about right to propell a 4" zinc solid shot 50 to 100 yards.

     Victor,   Oh, now I understand.  I certainly did not mean to imply that making the Spheroidal Chamber or the Ellipsoid/Concave type was going to be a piece of cake, just that it could be done and that we aim to make those, even if we have to start over or start over again!  We agree, it would be a few degrees of difficulty greater if you had to do this at the bottom of a deep bore as in a Gun.  That's part of our decision to work with a mortar on this series.  You can see what you are doing and you don't have nearly so much boring bar flexure to contend with.  It's not nearly as difficult as making a Welin Breech and Breech Block.  We are waiting for you to do that and then tell us how you did it!   

Tracy
 

[KABAR2]

I think in the case of concave and elips chambers it was less a case of machining in that time and more a case of casting..... in each case these are mortars and they appear to be cast guns so I would say the chambers were cast with little finish work to be done after the fact..... I have a feeling that these work on the same principle as the Hi/low chambers in modern 40 MM grenade cartridges

[seacoastartillery]

      KABAR2,      Of course this is true, Allen and we certainly agree with you that very little finishing would be necessary if you used this method to produce a mortar or gun with such a chamber.  We think in terms of machining, but we realize that there are more efficient ways to make a cannon tube. 

     Although it will be a huge yawn for many members, we think, for a few of you out there in cyberland, it may be interested to see what goes into the planning to create the ordnance for these chamber comparison experiments.  First  we decide on what type of artillery will suit the purpose of hassle-free experimentation.  We decide on a mortar.  Easier to make and easier to see what you are doing in process.  Next we decided that we wanted a moderate size mortar which will not exceed 150 Lbs. tube weight.  The bore size will be 4.00”, because we are familiar with that size and find it to throw an easily seen ball, but not so large a ball to require tremendous tube weight to negate recoil.  Next we have to decide on the distance we want the test projectiles to travel.  To cut down on walking, we decided on 50 to 100 yards rather than 200 or 300 yards.  How much powder do you need to propel  a solid shot weighing 9 lbs. to that distance? 

     Drawing on extensive experience with shooting my 1797 ½ scale 8” U.S. Land Service Siege Mortar made by South Bend Replicas in 1972, we decided on Fg powder weighing about 2 oz. , 875 grains avoirdupois.   Actually we want each chamber to hold as close to 4 cu. In. of Fg BP as we can get.  Accuracy in machining the various shaped chambers becomes very important.

     Next we have to determine the density of black powder of the Brand (Goex) and the granulation size (Fg) that we will be using in the tests.  So we made a measure that would throw four cubic inches of Goex Fg  black powder.  It’s dimensions are 1.128” Dia. X 4.000” long. Weighing this quantity we came up with 940 grains, so each cu. In. has a density of 235 grs. of Fg  BP.  So, you can see our standard charge for all these chamber efficiency experiments is a little bit over 2.0 oz, about 7% or 65 grs.  To help those of you out that want to build your own powder measuring scoops, here are a few more results:

Fg Goex      235 grs per cu. In.
FFg Goex    232 grs per cu. In.
FFFg Goex  238 grs per cu. In.
FFFFg Goex 236 grs per cu. In.

We machined a brass rod to the 1.128” I.D.  dimension X 4.000” long.  We have some copper ones too made from water pipe.  Avoid steel  pipe for obvious reasons.

     Sketches of the chambers will come next;  we are busy designing Brooke sights now, so our drafting facilities are being used.  Time to check and re-check calculations.  If the Concave Chamber is the most difficult to design and produce, then it’s the first one to figure out mathematically.  Our calculations are found below and we realize that there are several ways to do most designs and more ways to do the associated math.  This is our way, it may not be the best for your project.

     Every effort was made to make our ellipsoidal chamber as close to the Concave Chamber drawing shape in Muller’s book as we could.  The very 1^st thing to figure out is the volume of the entire ellipsoid shape even though a small portion of it is missing on the right hand side where the chamber meets the ball seat radius.


Concave Chamber from Muller’s book brought forward for shape comparison:




Sketch Here for Full Ellipsoidal Shape;  This is the Shape of our Concave or Ellipsoidal Chamber before Removal of the Elliptical Cone:

sketch from the website:   http://calculator.tutorvista.com/math/49/volume-of-ellipsoid-calculator.html





Axis Explanation and Better Axis Designation:  Yes, in our case B=C.     From Had 2 Know website:

                                                            http://www.had2know.com/academics/egg-surface-area-volume-calculator.html





Sketch Here for Elliptical Cone:          from this website,   http://www.exploration.grc.nasa.gov/education/rocket/volume.html


 
 
 
V1   Math Calc. for  Volume of Full Ellipsoid
V2   Math Calc. for  Volume of Elliptical Cone
V3  Math Calc. for  Volume of Modified Ellipsoid (Truncated Ellipsoidal Chamber)

                                                                                                                                                                                                         
V1   Formula and Calculations for Full Ellipsoid:
 
V1=  (2 pi/3) Asq (B+C)                                             A = .870"     B = 1.300"     C = 1.300"
V1=  (2x3.1416/3)(.870)sq (1.300 + 1.300)
V1=  (6.2832/3)(.7569)(2.600)
V1=  2.0944 x .7569 x 2.600
V1=  1.58525 x 2.600
V1=  4.122 cu. In.
 
 
V2  Formula and Calculations for Elliptical Cone:
 
V2=  ( pi x  dsq x  h)/6                                        d = 1.044”         h = .200”                                                 
V2=  (3.1416 x 1.090 x .200)/6                       
V2=  .685/6
V2=  .114 cu. In.

 
V3  Calc. for  Volume of Modified Ellipsoid
 
V3 = V1 – V2
V3=  4.122 - .144
V3=  4.008 cu. in.


     All of the other chamber shapes will be the same volume within 1/100 of a cubic inch.  This one is within 8/1,000 of a cu. in.  As we get closer to the time when these are made, we will provide some numbers for machining this chamber shape.  We will also have some machining process info such as Operational Steps like drilling, straight cylinder boring and radial expansion boring to create the Spheroidal or Ellipsoidal Chambers.  Sure, there is a lot of figuring before we can start to machine steel, but we are excited.  All this is new and different and these mortar inserts will be fun to make and use!  Can't wait!  Any questions?  Ask away.

Mike and Tracy



   
 
 
 

[keith44]

at the risk of sounding like the math geek my wife says I am,  thanks for posting the formulae for those volumes along with the links.

[oltom]

uuhh....well, and I thought making the wooden wheels was the tuff part in makeing my cannon!!!!!!!!

[seacoastartillery]

      Keith,   You are welcome.  I’m not a math geek, like my college roommate was, but I had to learn what I ignored in school to get an inspector’s job, so I did. That and 42 years of using it at least every week teaches you a few formulas and methods.  I know a little right angle trig, some basic algebra and a bit about proportion and ratios, that’s about it.  I bet you know tons more about math than I do!

     I think you are right, Oltom.  I haven’t made any of those yet.  Just thinking about making them stops me.  If you use just a little math beyond addition, subtraction and multiplication, you would be surprised what you can do.  For instance it’s handy to know that for every degree of divergence from a baseline, that another line is, for each inch along it from the vertex, a rise of .0175” can be expected.  In just 100 inches, a rise of 1.750” is apparent.  You can use this knowledge whether you are machining parts or doing carpentry.

     I am gathering a few materials and making a few preliminary sketches of the main tube for this series of experiments.  Actually, I like the old French tube featured in the depiction of the spherical chamber.  I think that would be an interesting exterior.  Please don’t expect that Mike and I will wear authentic costumes of that period when we conduct the firings!  We might be persuaded to use a replica of a French linstock from the late 1700s that was made by Harry Burdette of Burdette Metalsmithing and Design of Broomfield, Colorado.  What period is that tube anyway??  1600s, 1700s?


Here it is, brought forward for convenience.






This is the surplus 7.00” dia. X 29.00” long round of 4150 crucible steel.  Stock available for the test mortar’s exterior.






These are the 5.00”dia. X 29.00” long rounds of 4142, Rc 30 steel left over from 100 Pdr. Parrott development.  This is enough stock to make 8 chambers.

 



     We are just throwing a few numbers out to see if we can avoid buying any new steel when we make this main tube and the various inserts.  Looking at the old French tube in the woodcut above, I think we can use a portion of a 7.00” X 29.00” round of 4150 steel that was surplused when a customer ran into financial trouble last year.  Part of his garage and most of his large driveway was washed away when a nearby creek overflowed during a springtime freshet.  We returned his $5,000 deposit immediately.  We will not be making any more Brooke cannons so the steel is surplus.

     With a 7 inch O.D. and a 4.100” dia. Bore, a 1.97” dia. spherical chamber and a 1.25” dia. chamber to ball seat transition cylinder,  I think two rounds of 4142 pre-hard, Rc 30 that we have from early experiments on the 100 Pdr. Parrott Seacoast Gun, will fit the bill. They are  5.00” O.D.  and  29.0” long.   This should give us 8 pieces, each about 7.00” long, for making chambers.  Some dimensioned sketches will follow next.

Tracy