Moe Hip Drop questions

[Anonymous]

Judging by my last two posts, I'm only a "guest" now. However, if anyone cares to do so, check out Hip_Sections.pdf: Is the result of the calculation ½ Width × Plumb Backing Angle the “Hip Drop”? The revolved section view is the same as in the Hip_Valley_Sections.doc. This sketch also shows the plumb section and two methods of calculation. Regardless of which section is viewed, the Jack rafters (not shown) would “plane” or intercept the Hip where the shoulders of the ridge meet the plumb sides of the rafter.
I haven’t gone over the math with a fine-toothed comb, but so far the implications are:
The only way two spans can truly plane at a Hip-Valley is if there is a bevel or backing angle forming a ridge-trough.
The difference of this ridge height depends ONLY on the Hip-Valley rafter width, NOT the difference in length along the entire plumb cut.
There are consequences in terms of the Hip rise and run.
Leaving a backing angle out of the equation calls for a sacrifice in terms of accuracy. What I’m uncertain of is what is considered reasonable or acceptable practise?
The geometry of two equal Common spans meeting at 90° guarantees Plumb Backing angles equal to the Hip pitch angle. For comparison, I’ve included the sketch Irregular_Hip_Section.pdf where this is not the case. The sequence of calculations is the same in both diagrams. Total rafter depth has no bearing on the final outcome and is therefore not shown.

[Anonymous]

Sorry about that, folks!
Looks like "guests" can't edit post or add attachments.
Diagrams will be posted as soon as possible.

[Joe Bartok]

Here's the attachments referenced in the last two posts by the unknown "guest".
Hurray! I'm online again!

[R Birch]

Joe,

After taking a look at your two picture files above I think that the “Irregular_Hip_Section” will cause a little confusion if not just plain intimidate some other guys into not posting replies to your post. The Irreg Hip shown in your picture is also known as an Irregular Dog-Leg Hip. These are hips that are formed as you show from dual pitches meeting at walls joining at an angle other than perpendicular. These hips are commonly found on unequal sided Octagonal roofs like commonly framed over pop-out bays where the main bearing wall with windows is much longer than the 45 deg return walls to each side. There are other design scenarios that have these kinds of Irregular Hips too but overall they are not extremely common and for the sake of a discussion about “Dropping a Hip” I would like to suggest that this discussion start about Hip/Vals that are on Regular or Irregular Hips positioned over square corners like your first Hip_Section.pdf file illustrates.

Here are a couple of my response to what you believe your math “implies”

“The only way two spans can truly plane at a Hip-Valley is if there is a bevel or backing angle forming a ridge-trough.”

The ridge-trough can be real, (backed, or beveled on top), or imaginary, (Not backed). There is always a position that an unbacked hip can be placed to plane. It would most likely be at the same place the backed version would be placed but it would depend on how the back bevels were applied to the hip. If they were centered it will change, or shift slightly to the steeper side. If they were unbacked then they would be placed proportionately to plane, and the lesser pitch will always occupy more surface area of the top of the hip.

“The difference of this ridge height depends ONLY on the Hip-Valley rafter width, NOT the difference in length along the entire plumb cut.”

My response to this is the “difference” (or Hip Drop) is dependant on the Hip’s thickness. But it is only an apparent difference depending on you point of view. Viewing the Hip from a perpendicular position the backed hip will have an apparent difference in HAP. The backed Hip viewed from a position perpendicular to the common rafter, this apparent difference is not seen as it planes with the commons from this vantage point.

“Leaving a backing angle out of the equation calls for a sacrifice in terms of accuracy.”

I will disagree on this one. The unbacked hip/val can be place with equal accuracy.

“I’m uncertain of is what is considered reasonable or acceptable practise?”

I have found that in order to have roof components assemble in a “Snap together” manner that the cutting tolerances be kept as close to perfection as the boards are marked. If you don’t make any errors in your calculations, and the sawyer cuts it accurately, it will fit perfect.

I find that being able to accurately calculate, mark, and cut these Hip/Val rafters is essential to production Cut-Roof framing.

I hope to hear some other opinions and observations about this subject, as it is one of the more interesting aspects of roof cutting. It is sometimes confusing and controversial, but always interesting.

Edit; I forgot to say;

Btw, Great Post Joe!

R Birch

[Joe Bartok]

Richard, thanks for the response. I'm posting first in case I have trouble remaining logged in and lose this window of opportunity.
I'll read your post in more detail, and I'll be back ... if possible.
The Irregular_Hip_Section.pdf was unclear in terms of how the width ratios were calculated and the direction of view of the section. Here’s an expaned version, Irregular_Hips_Valleys.pdf, highlighting some problems or differences between Hips and Valleys.
Page 1: Irregular Valley rafter. The advantages of the method of scaling the rafter width as shown are listed on the drawing. This isn’t just theory. Been there, done that:
71/4/12 , 9/12 pitches meet at 90°
Two 9/12 Ridges, a 71/4/12 Ridge, a 9/12 Common rafter and two 521/32/12 Valleys converged at a center post with deadly accuracy.
Page 2: Irregular Hip rafter: Same scaling and calcs as the Valley rafter. Since a Hip rafter is in essence an “upside-down” Valley, the Deck angles seen in plan are measured at the eaves rather than the ridges.
The scale returns a consistent value for the Hip drop (Page 3). The down side is that calculations following the “natural” angles create problems when sizing the ridge widths. We cannot connect the points at the Hip ridge as we did on the Valley.
Exact Hip depth and ridge width are fixed in “two-by” framing and not a concern, but the math for working to reference lines as per the diagrams must to be understood before we can consider Hip drops and shifting the Hip. The math must also be consistent under any conditions. The arguments cannot be restricted to special cases where ridges-eaves intercept right angles or only equal pitches are permitted.
Page 4: Width scaling formulas.
Not shown in this drawing: The width ratios were re-calced using the angles at the Hip ridge line. The result is that the ratios are transposed from Main to Adjacent sides and a line can be drawn at right angles to the long axis of the Hip, connecting the working points as per the Valley drawing.
Another result is that we can kiss the equal sides and Hip drop calculations on Page 3 goodbye. As long as we don’t require equal Hip and ridge depths this is no big deal; the rafter can be shifted sideways about the ridge line to a more convenient place.
Related to all of the above is PENTAGONAL_ROOF.pdf. The sections on Page 1 illustrate the problem. The rafters are classified or named according to the manner in which the Backing angles are cut. These angles may be actual planes on the roof, or they may be theoretical working points, but either way they determine how the jack rafters “plane” with the … with what??? One rafter is a true Hip, the other four are a hybrid of Hip and Valley. We calculate a drop for the Hip, but what about the other four rafters? The problem can’t be ignored; these are 6 inch wide beams.
Somewhere in this mess there’s a consistent, logical answer to dropping and shifting Hips. To recap the givens:
Reference lines are known.
Working points are known.
Angles in the roof system are known.

[Joe Bartok]

Let's see if I can post this before I'm "involuntarily" logged out.

“Leaving a backing angle out of the equation calls for a sacrifice in terms of accuracy.”
Richard (and any other readers), just disregard that. I was thinking of the Hip or Valley without backing angles meeting the ridges. There's going to be a bit of a mismatch there, but in the case of two by whatever framing (or even wider sticks) it's going to be almost nil.

There is always a position that an unbacked hip can be placed to plane.
Agreed, and my reference to "inaccuracy" wasn't intended to include the planing of jacks at Hips-Valleys. Inspection of a section of such an intersection shows planing is possible, backing angles or not.

After taking a look at your two picture files above I think that the “Irregular_Hip_Section” will cause a little confusion if not just plain intimidate some other guys into not posting replies to your post.
Yeah, that thought crossed my mind as well.
I'm not trying to confuse or intimidate anyone. I'm trying to create framing program that will deal with these variables. Such a program must be able to cope with anything a potential user throws at it. If the variables are restricted to right angles only, or equal pitches, there's no point in spending time writing the code. Calcs such as the foregoing can be done with pencil and paper, or by geometric projection.
Nor was I looking for an answer in nit-picking detail. When I posted those diagrams, my thinking was that there are a lot of good, experienced framers (probably the best on this continent) out there who can look at the geometry in the sketches and see the solutions without a bunch of numbers. I did include the trig for anyone interested, but it's not strictly needed to come up with a strategy to deal with these roof systems.
I'm still studying your method of cutting the Hip. Since, as you say, it deals with Irregular pitches and Valleys, it might be the answer to the Hips (or are they Valleys) in the PENTAGONAL_ROOF.pdf. Now all I have to do is "translate" to trig so my computer can understand.

I have found that in order to have roof components assemble in a “Snap together” manner that the cutting tolerances be kept as close to perfection as the boards are marked. If you don’t make any errors in your calculations, and the sawyer cuts it accurately, it will fit perfect.

I find that being able to accurately calculate, mark, and cut these Hip/Val rafters is essential to production Cut-Roof framing.
Right on! It's neat to be able to precalculate and cut timber valleys, trusses, purlins, rafters and ridges, complete with mortises and tenons. Ship all this to the jobsite, and assembly everything. Well, one aspect of this isn't so good: it's indeed a "snap", in fact, it's almost boring! :twisted:

Thanks for the response Richard. I'm also hoping others will jump in and comment on this topic. Even if there's no "final answer", at worst we'll all gain a bit more insight.

[Joe Bartok]

Using the sketches in the attached Hip_Drop_Models.pdf as a guide, the Hip drop can be can solved trigonometrically on a CM or scientific calculator, laid out on paper with compass and straightedge, or on a piece of plywood with a framing square.
Note that use of half the width of the Hip rafter is valid only if the Common pitches are equal. Which brings me to my question for the day:
Is the calculation I have been using to scale the Hip rafter about the reference line called the “Hip shift” or “shifting the Hip”?
Btw, the angles labelled Main side deck angle DD, Adjacent side deck angle D, or Deck angles viewed in plan, are what you guys call “cheek cuts”, aren’t they? Could have picked worse names. How about “the dihedral angle between the plumb side face of the Hip rafter and the plumb side face of the Common rafter”? How does that sound? :twisted:

[R Birch]

Joe,

Those are some great illustrations!

Your last post and .pdf attachment really proves how confusing the Hip drop is while also proving how easy it is to solve for at the same time. But with my method it is not a concern. That is for 2/ framing w/o backing the Hip.

[Joe Bartok]

Richard, the method detailed in your photo essay is indeed elegant, to-the-point, and eliminates calculation. Just the type of applied knowledge that's needed on-the-job.
I'm trying to create a calculator, and my computer sucks. It doesn't "understand" geometry, so I still need the formulas to tell the computer what to do. The effort to "translate" to formulas is never wasted, in the process of writing a program or creating a worksheet, one gets very familiar with what's happening in terms of the geometry.
Another aspect of making a calculator is: How does the average person that's apt do use the calculator define the various terms? What do they expect to see? I think I'm clear on what's meant by "Hip drop", and will thus be able to include graphics that will likewise clearly define the term for the average user.
On to the next question (same question as the last post, actually):
Irregular_Hips_Valleys.pdf: The illustration on Page 3 and calculation on Page 4. Is this what is defined as "Shifting the Hip"?
There doesn't seem to be a lot of interest in this subject, but that's probably because my questions are nothing new to the people on this forum. People who frame for a living have dropped and shifted Hips a zillion times, and it's become a skill that comes naturally. I'm still on the "learning curve" and have to think everthing through in nit-picking detail.

[R Birch]

Joe,

Thanks for kind comments about my photo essay. I see you understand it completely. And I am so glad that you do.

When I first came across the terms “Dropping” or “Shifting” a “Hip” it threw me a “Learning Curve” too. I assumed that these terms suggested that the hip was misplaced to begin with so they were “Dropped” or Shifted” to correct this misplacement. In the end the “Drop/Shift” places the Hip/Val in the same place as the method I use. They are just different ways to get to the same place. I thought my way was simpler and created less confusion than the “Hip Drop” method. It seems that it depends on whose school of thought you subscribe to on this issue. I work from the outside line of plane and the HD works from the inside, or center, or arris, point of plane. The method I outlined years ago on some other forums was seemingly so simple that many guys scoffed at its feasibility to begin with. They are not likely to join in more forum discussions because the subject has been beaten to death.

In the end again it is only the concepts of perspective that are different, the rafters created are virtually identical. But I still got to think that my method makes them easier. (For 2/ conventional framed Roofs, not the log homes you are accustomed to building. But it seems logical that it would have its place there too. I just don’t have any experience with log homes though.)

[One Artisan]

Joe some great stuff!!! But how do you get the (backing angle)???? Or schould I say how do you detrmine the angle??

[Joe Bartok]

One Artisan
There are dozens of formulas for the Backing Angle. The following formula is the best known:
Let's call the angle in plan measured between the Hip Run and Eave the Plan Angle (or Deck Angle), and the angle of the Hip rafter with respect to level the Hip Pitch Angle. (For a Valley rafter, the Plan Angle is measured between the Valley Run and the Ridge Line as viewed in plan).
Backing Angle = arctan (sin Hip Pitch Angle ÷ tan Plan Angle)
The above formula is based on this Geometric Interpretation of Backing Angle (http://ca.geocities.com/xpf51/PROJECTIONS/BACKING_ANGLE_MODELS.pdf)
Alternative formulas are:
Backing Angle = arcsin (sin Common Pitch Angle × cos Plan Angle)
Backing Angle = arccos (cos Common Pitch Angle ÷ cos Hip Pitch Angle)
That's just a few of the formulas. If you just want the angle without going through the calculations: Roof Framing Angles (http://ca.geocities.com/xpf51/HVFRAMING/FRAMING_WP.html)
For those who want to learn the theory behind the formulas:
Log Roof and Timber Framing and Joinery Angles (http://ca.geocities.com/xpf51/)
or
Hip and Valley Roof Trigonometry (http://ca.geocities.com/xpf51/LOG_AND_TIMBER_FRAMING_ANGLES/)
Enjoy, and if you have more questions, fire away!