Hip rafters are the main structural timbers that form the change in direction in a hip assembly. Typically, these rafters span from the corner of the wall plate to the intersection of the crown rafter and the last common rafter at the apex of the roof. Once installed, the deeper structural hip rafter supports the top cuts of the jacks rafters that continue the on centre layout of the roof as it follows on from the last common rafter. For an approximate reference, a modern roof that features 6” common rafters will typically involve 8” hip rafters. At the apex of the geometric intersection, the rise of the total roof structure is fixed based on the span of the wall plates and the pitch of the roof. When cutting a hip rafter, the plumb and seat cuts do not match the angles of the common rafters. Whilst the hip rafter matches the plane of both rakes of the roof that it supports, when we take the hip rafter on its own, the pitch is lower than the pitch of the common rafters. The hip rafter rises the same amount as the common rafters to meet the geometric intersection, but travels further horizontally from the corner of the wall plates. This lengthens the hip rafters and alters the angles that we must cut. The run of the hip rafter is equal to the value of the hypotenuse of a right-angled triangle with the 2 sides equal to the run of the roof.

There are a handful of methods to calculate this new angle for the plumb cut of the hip rafter. The roofing reckoner, as well as most roofing calculators will clearly display the angle of the top cut of the hip for any given pitch of the roof. Alternatively, roofing squares often display the relevant angles to calculate the angle, in a similar way to how the plumb cut of a common rafter is calculated. Most speed squares also feature a secondary gauge that provides the bevel angles for hips for most of the common roof pitches. To demonstrate the point, we can look at a 45 degree pitch roof. We know that the pitch of the rafters are 45 degrees, and that the plumb cut matches this angle to meet into the ridge board correctly. When it comes to cutting a hip to fit a 45-degree pitch roof, the plumb cut angle of the hip rafter is more shallow, at 35.5 degrees.

With this angle marked on the timber to produce the top cut, we must now create the two edge bevels on the plumb cut that receive into the geometric intersection. On plan, this edge bevel is 45 degrees, and can be cut easily as a compound cut with a chop saw or skill saw by setting the blade angle to 45 degrees and cutting to the line of the plumb cut. This must be done on both sides to achieve the dual edge bevel that creates a point at the centre of the timber. The resulting compound cut will always be correct provided that the plumb cut was accurately followed on a 45 bevel. The edge bevels of the hip rafter plumb cut are at 45 degrees to the plumb cut itself.  

This being said, when cutting this bevel by hand with a handsaw, the layout is not marked at 45 degrees on the timber. Marking out a 45-degree angle and cutting this with the plumb cut will result in a stubby edge bevel that does not receive well into the intersection. To accurately replicate this compound cut, we must employ a trick to find the angle of the edge cut.  

Firstly, make a hip rafter plumb line at the top of the timber. On the side of the timber, travel perpendicularly away from this plumb line the thickness of the hip rafter and create another plum line from this point. Square both of these plumb cuts across the top thickness of the timber. Connecting these two lines corner to corner will create the correct side cut angle to cut to. Following this angle with a handsaw can be difficult to begin with, but with practice it can be easily cut, especially if we position ourselves above the timber.  

With the plumb cut made, we can move onto marking out the seat cut. Technically speaking we could simply calculate the length of the hip in the same way we would calculate a common rafter, using a set of specific hip rafter tables or a hip rafter calculator. This being said, any irregularities in the exact position of the geometric intersection, or the position of the corner of the wall plates can cause this calculation to be incorrect. As such, there are alternative methods we can use to achieve accuracy in our endeavour. Two primary methods are typically employed, both in varying circumstances. Regardless of the method, the first step is to obtain a critical measurement. On the common rafters, the vertical distance between the top of the rafter and the seat cut of the birdsmouth notch is known as the backing. We need to measure this backing, as regardless of the pitch of the roof or the length of the hip rafter, this backing distance is shared between the common rafters and the hip rafter. This ensures a consistent height and angle around the lower portion of the return. 

With this measurement in mind, we will look at “dropping in” a hip. The first step is to cut off the corner of the wall plate to create a good bearing for the seat cut of the rafter. By placing an offcut of timber on the corner of the wall plate, aligned diagonally with a speed square, we can mark the corner of the plate where we need to remove the material. We may also need to chip part of the masonry off below the plate to accommodate the hip seat cut. In doing so, we can ensure that the seat cut will be fully seated against the wall plate.  

If we place the uncut hip timber on this cut off corner, it will want to drop down by a specific distance for the thickness of the back to be correct. We shall call this amount “x”. If the timber at the plate wants to drop down the depth of the birdsmouth, then in order to align the hip in the correct position at the top of the roof for us to mark the location of the seat cut, the top should be sat above the hip intersection by the depth of the birdsmouth. To mark this depth at the top of the hip timber, we must measure upwards from the bottom of the hip rafter plumb cut, the distance of “x”. If we sit the timber on the corner of the plate, with the marked plumb cut sitting the correct distance above the hip intersection, then the hip rafter is situated at the correct angle, higher than it should be by the depth of the birdsmouth. Using a straight edge or square, we can plumb a line up the hip rafter at the point where it meets the corner of the wall plates. This line is the back of the birdsmouth.

Taking this timber down again, we can mark out the rest of the birdsmouth. Measuring down from the top of the hip the thickness of the backing, we can square our seat cut across to produce the seat cut. By cutting out the waste, we have a full hip that is ready to be seated in place. Note at this point that the cutout may be more than ⅓ of the thickness of the hip timber - this is okay and is very common. Due to the varying thickness of timber and alternate angles involved in forming a hip, the birdsmouth may be more than 1/3 of depth of the timber. In this instance, we can add additional support through a secondary birdsmouth, though the extra thickness of the hip rafter compared to the common rafters means that it is generally still structurally sound.   

The hip can then be dropped into place and should be a perfect fit. The top corners of the hip should meet the edges of the last common rafter and the crown rafter. This method is ideal for single length timbers that can be easily handled by a few operatives on the roof. However, when hip rafters grow in length or thickness, lifting them in and out becomes impractical. Often in large, hipped roof loft conversions/attic spaces, hip rafters are implemented in the form of double or even triple bolted timbers, with or without flitch plates, to increase the load bearing capacity of the structural assembly. In these instances, dropping the hip in would be too much unnecessary work. As such, we must use another method to actually measure the length of the hip to cut it before its installation. This method is also straightforward, and is on par with dropping the hip in terms of effort.  

To start with, we must cut the corner of the wall plate off again as we did in the other method. Note here that we must always cut the plate off at the thickness of the hip rafter. As such, if the hip rafter is a double timber, we must mark out a double timbers thickness to remove from the wall plate, so that the birdsmouth of the hip rafter fully seats against the wall plate. Next, we must cut a block that is the length of the backing of the common rafters. We will sit this block on the edge of the wall plate, where the corner was cut off. The top edge of this block in this position represents the top edge of the hip rafter at the plumb line of the birdsmouth. With the help of another operative, we can take measurement with a tape measure from the very apex of the hip intersection all the way down to the back of this block. Using this measurement, we can cut the birdsmouth of the hip rafter out at the correct position along its length. If accuracy was maintained during both the measuring and marking processes, the hip rafter should sit correctly in place with no adjustments required.  

Hip rafters that are supporting a large load may require additional bearing and bracing where the birdsmouth sits over the corner of the wall plate. Often, a timber angle tie is installed at a 45-degree angle, spanning the corner of the wall plates. This timber is typically 4”x2” or 6”x”2. The timber tie is fixed with fasteners to the wall plates to prevent them from spreading apart at the corners under the load of the hip. This timber can also provide additional bearing to the hip rafter if the hip end is supporting a large load, or if the birdsmouth is oversized on the hip rafter. A secondary shallower birdsmouth is cut to receive over the timber angle tie. In accordance with the NHBC standards, metal restraint twist straps must be installed from the hip rafter to the timber angle tie to prevent the bottom of the hip rafter from moving outwards away from the wall plates.  

Another aspect of a hip rafter to consider when forming a hip end is the potential requirement of a back bevel on the top edge of the hip rafter. When two different planes of a roof meet each other at a hip or valley, the angle is known as a dihedral angle. This dihedral angle is the name given to an intersection of two planes that are themselves angled in multiple directions. On plan, this angle meets at a perfectly sharp line. In reality, when applied to an actual hip roof, the modern method of installing a hip sees a full width timber below the true line of the roof. As we can see in the illustration, the very edges of the hip rafter are true to the different planes of the roof, whereas the width of the timber sits below the dihedral angle intersection. For a roof system that features battens meeting at the hip, covered by ridge tiles, this solution is perfectly adequate, and provides a stellar result every time. However, in some instances, such as where the hip rafter is much wider than a single timber, or where the roof will be sheathed with plywood, this lack of supporting material can cause issues. As such, the true profile of the roof, the dihedral angle of the roof, can be cut or planed onto the back of the hip. This angle brings the hip rafter back into true alignment with the planes of the roof, creating adequate support for the desired outcome. To set out this angle the process is as follows.

The plumb cut and dual edge bevels of the hip rafter are cut first for the sake of simplicity. A measurement of half the thickness of the hip rafter is taken. This distance is measured backwards from the plumb cut on the side of the hip rafter, and another plumb line is drawn. A perpendicular line is made with a square from the top of the secondary plumb line to the primary plumb cut. The point where this perpendicular line meets the plumb cut represents the lowest edge of the dihedral back bevel. This distance can be marked all the way down the length of the hip rafter. A plane or saw is then used to shape the back bevel, from the centre of the hip as the highest point to the lowest point at the mark we have just made. This bevel is made on both sides of the hip rafter to create the full dihedral angle. With this back bevel cut on the hip rafter, the presentation of the hip rafter changes slightly in relation to the other timber components. With this angle on the hip, the very top of the hip rafter plumb can meet the apex of the ridge intersection. When installed, the top of the backing bevel will follow the slope of the last common rafter and the crown rafter. The jack rafters will meet the low edge of the back bevel, with the angle of the dihedral bevel continuing the slope of the jack rafters to the apex of the bevel. The hip rafter is still sat in the same position within the roof, but the back bevel provides additional material where there was none before. To accurately drop a hip that features a backing bevel, the distance of the common rafter backing must be measured down from the lowest point of the backing bevel at the hip rafter plumb cut, as this is representative of the top edge of a regular non-backed hip rafter. The same backing distance is then measured up from the bottom of the plumb cut as usual.

Hip rafters that are formed from 2 timbers have a single edge bevel cut on each timber, with the two halves coming together to form the dual edge bevel required at the top of the hip rafter. 

Another implementation of this dihedral angle may come into play with timber framed constructions that feature large timbers as hips, as well as in joinery grade garden rooms and such. 

This method only works for hip rafters that are on a true 45 degree on plan. We will look at the process of marking out the backing angle of irregular hips in the later stage of this roofing section.