iwonder wrote:Balsaman, glancing at your loads for a C division boom, it seems like the tension force is wrong... How could the tension member be under less force than the compression member when all the force in the compression member has to be countered by the tension member? Could you post your math?
Good pickup- with Christmas eve things going on, I switched tension and compression #s for C; edited that post to correct; 40kg compression, 44 tension (actually 42.7kg). Tension and compression are not equal. I'll try to get the math posted today.
Ahh, much easier than writing it all out myself-
here's a lecture on static equilibrium that covers it nicely: http://www.ic.sunysb.edu/Class/phy141md ... ectures:20
See notes, and layout of the problem, and the lecture discusses it starting at a bit before 11 minutes.
As you'll see, both tension and compression forces are a function of the angle at the distal end (the angle between tension and compression member. Let's call that angle theta.
Compression force is the load (15kg) (mg) divided by tan theta, and tension if the load divided by sin theta. They are different, and tension is > compression.
For a boom with a length of 40, and a height of 15, theta is 20.556 degrees.
tan theta is 15/40 (=0.375); sin theta is 15/42.7200 (=0.35112)
15/0.375 = 40.0kg compression
15/0.35112 = 42.7204 kg tension. (So, my "44kg is a bit high)
retired1 wrote:My computer analysis program says that 3/32 bass wood will carry the load. It fails at about 16.5kg.
That also assumes straight grain bass wood and good gluing techniques.
Just curious about that program- what underlying data's driving it. Is the input just "bass", or bass at a specific density? Bass density range is significantly less than that of balsa, but there is a range, and tensile & shear strength varies across that range. In 3/32nds, most (~60-70%) pieces fall in the 1.5 to 1.6 grams per 24 inches range; at the extremes, a few pieces out of a hundred as light as 1.3-, and as heavy as 1.8+. Done quite a bit of compression/buckling testing on 3/32nds bass, but only 1 tension test years ago; 1.5 gr/24" at about 25kg..... Consistent with Aia's input earlier this year of a pair of 3/32nds bass t-members (density not specified) being conservative- stronger than needed; with a significant safety factor. For a B-boom, way conservative.... actually, way conservative for a precisely aligned build. Certainly strong enough to tolerate a fair amount of off-axis/tortional loading
I used the weakest bass wood in the program which is 27pound per cu ft.
There are options for 31.5 and 36.
While looking at it, I found one place that said 28.8 newtons, but the tension members both failed in one of the iterations at the 16.5 kg. (actually, 16.4kg) I quit asking the program for information at that point.
iwonder wrote:Balsaman, glancing at your loads for a C division boom, it seems like the tension force is wrong... How could the tension member be under less force than the compression member when all the force in the compression member has to be countered by the tension member? Could you post your math?
Good pickup- with Christmas eve things going on, I switched tension and compression #s for C; edited that post to correct; 40kg compression, 44 tension (actually 42.7kg). Tension and compression are not equal. I'll try to get the math posted today.
Ahh, much easier than writing it all out myself-
here's a lecture on static equilibrium that covers it nicely: http://www.ic.sunysb.edu/Class/phy141md ... ectures:20
See notes, and layout of the problem, and the lecture discusses it starting at a bit before 11 minutes.
As you'll see, both tension and compression forces are a function of the angle at the distal end (the angle between tension and compression member. Let's call that angle theta.
Compression force is the load (15kg) (mg) divided by tan theta, and tension if the load divided by sin theta. They are different, and tension is > compression.
For a boom with a length of 40, and a height of 15, theta is 20.556 degrees.
tan theta is 15/40 (=0.375); sin theta is 15/42.7200 (=0.35112)
15/0.375 = 40.0kg compression
15/0.35112 = 42.7204 kg tension. (So, my "44kg is a bit high)
The numbers for the tensile and compressive forces discussed above (yesterday) are for “right at the rules” dimensions- for both B- and C-booms, a length from the wall of 40cm; for B- a height of 20cm, and for C-, a height of 15cm. There are a couple of design factors- options for the geometry of your layout that can change these numbers a bit. Optimizing how you handle these options will minimize the forces. Minimizing the forces means less/lighter wood, improving your score. For those of you who have had some exposure to physics, and the basic trig in the formulas for calculating these forces, and who working to refine/improve the efficiency of a basically good design- some things and numbers to consider. For those, especially B-div folk, who may not yet have been exposed to this science and math in class, you don’t have to understand the why, and how of the calculations that can be done; the conclusions/the endpoints; the what works better than something else, can (and should) guide you in smart directions- help you get to a more efficient approach; you can use the information even if you don’t fully understand it.
We’ve seen and discussed at some length, how, and that, the tension and compression forces put on the basic members of a boom when you hang a load on the end depend on, and vary as a function of the angle formed between the tension member(s) and the compression member(s) at the end the load block sits on – the “distal end.” Let’s call that angle “theta.”The narrower/smaller that angle is, the greater the forces for a given amount of load; the wider/bigger that angle is, the lower the forces. The lower the forces, the less wood/weight it takes to hold up to those forces; the less wood/weight, the better your boom scores…..
The two factors/options that affect the size of this angle are these:
1) Where, relative to the centerline of the three bolt holes on the test wall, the tension members intersect the wall- how “high” your boom is. If you position the wall end of the tension member(s) on the side(s) of the bolt(s) – let’s call that “side-mounted” - , your height is at/very close to the height of the bolt hole centerline above the bottom contact line (15cm for a C-boom, 2cm for a B—boom). If you position the tension member(s) so that they run over the top of the bolt/washer – let’s call that “top-mounted” – you get more height, and theta is increased. To get enough glue area to work, holding the ends of the tension member(s) in your “base plate(s), you want some reasonable thickness to the base plate(s)- as you increase that thickness, the point/height at which the tension member intersects the wall increases- you get more height (and a larger theta)- that gives you lower forces.
2) How much of a “side angle” the tension members are at. Looking down from above- in the simple case of a single compression member, with a single tension member directly above it, both members are in a single plane that is perpendicular to the wall. If you look at two tension members (keeping a single compression member), running from two bolt holes, the vertical planes for these tension members are at an angle to the test wall. Looking at the vertical plane down from the tension members, the right triangle formed is where the tension member is the hypotenuse, the side opposite theta is the height, and the distance from the distal end to the wall is the length. Because both the length and the hypotenuse are longer than when this triangle is perpendicular to the wall, theta is smaller, so the tension force in the tension member is greater.
So, for both B-booms and C-booms, the comparative numbers for the tensile and compressive forces at a full, 15kg load… These are based on a simplified, 2-dimensional analysis- looking at the right triangle formed by a single tension member extending down at an angle from a bolt to the outer end of the boom arm- the compression member – with the compression member going back (horizontally) to the testing wall. These calculated forces give you numbers for booms with two tension members and two compression members (the arrangement seen in Aia’s discussions, and most of the booms in the photo gallery- the most common configuration used) – take the forces for one tension member and one compression member, and divide by 2.
So, for geometry right at the rules dimensions – for C- height=15cm, length=40cm, tension member length (the hypotenuse of that right triangle)=42.72cm; for B—height=20cm, length=40cm,T-memb length=44.72cm. This would apply if your tension members are positioned so that they intersect/come to the wall at the level of the bolt hole centerline (i.e., 15cm above the lower contact line)- “side-mounted” tension members. In both cases, this assumes either a single tension member (and single compression member), or two tension members running parallel about ¾” apart-running off the sides of the bolt head or washer, with either a single compression member, or two close together, so T-members are running parallel.
This assumes:
For C- Ten= 42.7kg – for 2 T memb and 2 comp memb= ½ that = 21.35kg tension each
Comp = 40.0kg – for 2, ½ that = 20kg each
For B- Ten= 33.54kg – for 2 T memb and 2 comp members= ½ that = 16.77kg tension each
Comp = 30kg – for 2, ½ that = 15kg each
Next, for “top mounted” tension members (and including a “clearance safety factor” of 1mm) – length from wall to center of load block = 40cm+1mm=40.1cm, distance from bolt hole centerline down to lowest contact at 15cm-1mm=14.9cm below bolt hole centerline. This includes/is based on a ½” thick “wall block”, so the washer is out from the wall by ½”, and the tension member(s) run so that they are just clearing the top of the washer. For a C-boom, that means they actually intersect the wall 1.75cm above the bolt hole centerline. So, height=16.65cm, length=40.1cm, T-memb length=43.2cm; for a B-boom, they hit the wall 2.15cm above the bolt hole centerline. So, height=22.05cm, length=40.1cm, and T-memb length=45.76cm
In both cases, this assumes either a single tension member (and single compression member), or two tension members running parallel and close together, off the top of the washer, with either a single compression member, or two close together, so T-members are running parallel.
For C- Ten= 39.1kg – for 2 T memb and 2 comp memb= ½ that = 19.56kg tension each
Comp = 36.1kg – for 2, ½ that = 18.05kg each
For B- Ten= 31.1kg – for 2 T memb and 2 comp members= ½ that = 15.55kg tension each
Comp = 27.3kg – for 2, ½ that = 13.65kg each In both cases (B- and C-), the forces are approximately 10% lower; not a lot, but 10% is 10%. If the forces are 10% lower, you should be able to use something close to 10% less wood/weight if you “go over the top.”…..
Next, with the 1mm clearance safety factors, for top-mounted tension members that run one to the center bolt hole, and one of the side bolt holes (10cm apart) – and with a compression member separation of 5cm (2 compression members 5cm apart). This also applies to running the two tension members (top-mounted) from a single bolt hole, with a compression member separation of 5cm. These tension members are running at a ‘side angle” to the wall. Compression stays the same
For C- Ten= 39.61kg – for 2 T memb = ½ that = 19.80kg tension each
For B- Ten= 31.48kg – for 2 T memb and 2 comp members= ½ that = 15.74kg tension each In both cases, on the order of about 1.3% more force than with tension members perpendicular to the wall- not very much. This much off-set really doesn’t hurt you, even though it’s not optimal.
And last, for top-mounted tension members (w/ the 1mm clearance safety factors) that run to the two outside bolt holes (20cm apart) - with a compression member separation of 5cm (2 compression members 5cm apart)). The side angle of the tension members to the wall is greater than in the case above
For C- Ten= 42.1kg – for 2 T memb = ½ that = 21.05kg tension each
For B- Ten= 33.28kg – for 2 T memb = ½ that = 16.64kg tension each In both cases, a bit over 7% more force than with tension members perpendicular to the wall- depending on how hard you’re pushing for/looking for more efficiency, maybe worth avoiding. Not only do you have this +7% higher force, the length is about 3cm (each) longer, so 6cm more wood.
