A look at the differences.

Tangent handrail is not an exact science, even though the geometry used when drawn into a CAD programme is accurate to a thousandth of an inch, the principle is there to guide one through the setting out of the staircase to take the geometric handrail and then to give the handrailer a good indication of the geometry through which the handrail will flow.

The final interpretation of the tangent handrail is down to the individual craftsman, many of the tips and tricks would be difficult to explain in books or videos and it is only through experience that the skill may be fully learnt.

Computer aided design software will be a lot more accurate than traditional drawing methods but will not allow for the interpretation made by the craftsman in production, hence when using CAD software the tangent system may throw up anomalies that drawing using the tangent handrail system will not show.

Here we will look at some of these anomalies, why they happen and how to interpret them in the drawing stage, to be able to send these drawings to CNC for production.

By understanding this, the CAD operator can interpret the tangent handrail components much as the craftsman would on the bench.

This will then allow for the tangent system principles, to be used in setting out the staircase for production.

There is also an opportunity with modern-day CAD to refine the tangent system making it a better basis for staircase setting out.

180º wreathing turn – half going.

Here we will compare how the tangent handrail and CAD drawn handrail works going through a 180º turn, with the handrail centre lines set at 1/2 a goings space, In the tangent method stretchout this would keep the handrail at the same pitch through the turn as down through the straight flights.

Dimensions for this example.

In this example we will use a going of 10″ – 254mm and a rise of 7″ – 178mm as shown in this plan view of the turn.

This will give a handrail centre line offset of 5″- 127mm

A handrail centre line radius of 2 ½” – 63.5mm

Diag 1.

Diag 1. Plan view of the turn.
Diag 1. Plan view of the turn.

A video introduction to this article.

the plan view we are using, with the stretch out for the tangent system.

Part 1. Tangent handrail system.

Part 2. CAD system.

Part 2a. The tangent handrail stretch out in CAD.

Part 3. Tangent principles adjusted for CAD.

Part 3a. The new plan view for CAD.



Part 2. CAD system, tangent intro.

Part 2a. The tangent handrail stretch out in CAD.

How the tangent handrail stretch out looks when overlayed onto the CAD stretch out of the same floor plan.

Part 2b. Adjusting the tangent handrail stretch out in CAD for CNC.

How to adjust the handrail centreline flow to mimic tangent handrailing.

Part 3. Moving forward – using tangent principles in CAD.

How to design the handrail and staircase using the tangent principles in CAD.

Part 1 – Tangent handrail system.

Stretchout using spring lines.

Using the dimensions above we can draw the stretchout as used in the tangent system. Diag 2.

Here you can see the handrail pitch line keeping the same pitch through the turn and hitting the correct points at the intersection of rise and going.

This keeps the risers in line and the distance between the two flights is easily calculated.

Tangent stretchout showing handrail pitch through turn.
Diag 2. Tangent stretchout showing handrail pitch through turn.

Stretchout using radius through turn.

In Diag 3. We can see the difference in length between using the tangent boxes for the going length and the actual handrail centre line radius.

The tangent boxes will equal the sides A, B and C.

These will equal one going as we are using 1/2 a going in between handrail centre lines.

Therefore A + B + C = 10″ – 254mm

While the radius D through the handrail centre line will equal 1/2 the circumference of a 5″ – 127mm Ø circle.

Therefore D = 7 13/16″ – 199mm

The difference between the tangent box outline and the actual handrail centre line length is 2 1/8″ – 55mm.

Tangent boxes v radius
Diag 3. Tangent boxes v radius

Difference in stretchout.

Here we see what happens to the handrail centre line, when instead of using the tangent boxes as the going, that are used for drawing the handrail in the tangent system, we use the actual circumfrance distance through the turn as the going length. Diag 4.

As you can see there is a difference in height and the handrail is approximatly 1 1/2″ – 38.5mm to low, as it does not travel the distance required to lift it to the correct height.

Tangent handrailers would deal with this in the manufacture stage, a slight ramping of the lead in straight both: Softens the start of the turn and makes up for the deficit in height.

This can be allowed for in the falling molds or often done by eye once the parts are dry assembled, before molding.

With CAD and CNC this is not an option and has to be dealt with before the big button is pressed.

The verticle difference in height.
Diag 4. The verticle difference in height.

The 180º wreath showing ramp.

Here is a 180º pitch to pitch wreathing turn.

In this picture you can see where the turn has been twisted at the central joint, to allow the wreathing turn to come to height.

As this has increased the pitch through the turn, you can see the ramp that has been shaped in to the top of the turn; to correct the pitch back to the correct pitch for the flight.

The same has happend at the lower end, with the under ramp being shaped in, this is hidden behind the spindle but does do the opposit to the top half of the turn.

180º p – p handrail turn showing ramp.

Correction in pitch to gain height.

As we now know the deficit in height, it is possible to add this into the turn. Diag 5.

This is done by increasing the exit rise “A” by the amount of deficit “B” and then drawing a new pitch line “C” from the entry rise tangent “D” to the top of the new addition “E” that is equal to “B” in length, over the exit riser line.

This will be the new pitch used to get the face molds and the falling molds.

This will acheive the height required without having to build in ramps and keep the springing points for the 180º turn over the riser lines.

This is one way of correcting the turn length for CNC production.

Pitch adjustment through turn.
Diag 5. Pitch adjustment through turn.

How to keep the handrail at a true constant pitch.

The new plan view.

With the information above we can calculate the Ø required or the distance between handrail centre lines to keep the handrail at a constant pitch through the turn.

This is done by simply dividing a going by Pi.

Therfore 254mm ÷ 3.14 = 80.85

So instead of setting the handrail centre lines 125mm apart, we now set them at 161.7mm apart, this increases the well size but allows the turn to travel the distance required to gain the height required for the handrail to join at pitch and removing the need for ramps in the lead in straights.

In Diag 6. we see the new plan view where the radius circumfrance equalls the same distance as 1 going,

This shows that the handrail pitch as drawn for tangent handrailing through the turn, is a lesser pitch than through the flights, this however allows the handrail centre line travel to be equal to 1 going keeping the true pitch constant.

Diag 6. The tangent boxes allowing for the handrail centre line to equal 1 going.

The pitch adjusted to handrail centre line radius.

In Diag 7. the pitch line has been drawn to the radius distance “D”.

Here you can see that although in the tangent system the pitch shows as becoming more gradual, in effect it stays at a constant through the turn, allowing for the correct height to be acheived as the handrail centre line length of run through the turn is equal to 1 going.

1 going radius pitch.
Diag 7. 1 going radius pitch.

The more obtuse the angle, the smaller the height discrepency will be.

The more accute the angle the greatet the height discrepency will be.

Part 2 – CAD system.

Here we have a look at the same situation but in a CAD programme. We will use the same dim’s again but this time unroll the surface to create the stretch out.

With an understanding of the tangent handrail principle, it is possible to adopt it and adapt it to CAD drawing, the drawings can then be used to create true tangent handrailing or recreate the geometry used by the handrailer.

There are a number of different software options, I use Rhinoceros 3D for these examples but the process will be the same in any software.

I am not the worlds best at CAD and there may be better ways to do this but hopefully it will give you an idea of what to aim for when drawing for tangent handrail parts.

We will also be adding 3D models.

Part 2a. The tangent handrail stretch out in CAD.

Plan view.

Using the same plan view and rises as per the tangent sample, we can loft a surface up through the well.

In Illu 1. the plan view is drawn out with the surface set over the handrail centre line.

I have indicated the position of the spindles and nosings just for clarification.

Handrail centre line surface.
Illu 1. Handrail centre line surface.

Constant pitch through turn, tangent system.

In this example Illu 2. I will use a surface to represent the handrail centre line in plan and project lines representing the rise, goings and handrail pitch, (in yellow) onto that suface.

I have included 3d models to download, for anyone who wants to follow this demonstration.

Download files.

These files are created from Rhino3d, should the file type you require not be here, rhino3d is avalable as an evaluation download, this will allow you to open the rhino 3dm file and gives a large number of file types that it will save as.

Try this full version for 90 days. After 90 days saving and plug-ins stop working, unless you buy a license.

Illu 2. set up.
3D model available for download.

Download model.


2-unroll-surface-tangent-boxes-3dm.zip Membership Required: Professional


2-unroll-surface-tangent-boxes-stl.zip Membership Required: Professional

Unroll the surface.

With the plan view elevated up around the well, we can draw a line up along the edge of the risers and across the goings or around the going for the radius in the half pace landing.

We can then unroll the surface with the riser and going lines, this will in effect produce a stretchout of the staircase onto the unrolled surface.

To keep a track on the surface orientation I have cut the top corner off.

In Illu 3. you can see the surface unrolled with the rises, goings and handrail pitch lines drawn on.

This shows that while the handrail pitch lines are sitting in the correct position on rises 1 – 4 and 6 – 8 when extended over going 5 they miss each other by the vertical distance “C” of 1 1/2″ or 38.02mm

This is due to the way the tangent boxes work if we measure the distance around the three sides of the tangent box we have 10″ 254mm Dimension” B”, when measuring this distance “B” from riser 4, the pitch line coming up from rises 1 – 4 reaches the correct rise height.

As the CAD software will open the stretch out using the circumfrance of the turn with a radius of 2 1/2″ – 63.5mm the CAd software will use this as going 5 and therefore rise posistion 5 is not set at the distance required 254mm to gain the full rise heigh at pitch but is set at the distance of 199.49mm instead Dimension “A”.

Hence the heigh discrepency of 1 1/2″ 38.02mm

Tan on cad stretchout.
Illu 3. Tan on cad stretchout.

Tangent stretchout overlaid onto CAD stretchout.

When we take the tangent stretchout and overlay it onto the unrolled surface, the difference is evident.

In Illu 4. I have set the tangent stretchout alongside the unrolled surface and copied the riser and pitch lines over onto the unrolled surface so show the difference.

In the tangent stretchout the pitch line hits all the correct points, when laid on the unrolled surface it will only hit the correct points one side or the other of going 5.

The difference in going 5’s length between the tangent and CAD software being obvious.

Illu 4. Tangent pitch line overlaid on CAD

Add ramps to flow round wreathing turn, Tangent.

The tangent handrailer will resolve the height discrepency in one of two ways.

  1. When drawing the falling molds, ramps will be added in both top and bottom to blend the tangent drawn wreathing parts into the straights either side.
  2. The straight that is added during the making of the wreathing parts will have height added on and the handrailer will shape the the ramps in by eye.

Which ever way this is done the ramp will flow past the springing lines and into the turn itself.

This makes the ramps very subtle and only the trained eye will pick up on these.

The straight lead in that most handrailers would use, is about 1/2 a going, therefore the first thing you need to do is trim the straights either side of the turn, back by half a going. Illu 5.

By cutting the straight rail back by half a going and then using blend curve to join the 2 straights together Illu 6. before flowing the pitch line back around the handrail centre line surface, the CAD drawn part will give a very close interprtation of the hand carved turn.

Illu 5. Trim straights.

Join the two pitches on the stretchout.

With the two ends trimmed back, a line may be descibed between them and in line as they meet.

In Rhino the blenc crv command will do this, this will create an “S” shaped bend betwen them. Illu 6.

Blend pitch lines.
Blend pitch lines.

Project back onto plan surface.

Once the two pitches have been connected, they can be projected with the curve for the turn, back onto the surface.

This will then give you the flow for the handrail centre line, that will closely mimic the handrail being traditionally carved using the tangent method by a handrailer.

To do this use the flowalongsrf command, select the pitch line with riser lines to confirm the turn is sitting in the correct postion, select the corner of the surface where the corner is cut off, then select the surface over the plan view by the corner that is cut off.

Part 3. Tangent principles adjusted for CAD.

With an understanding of the principles above this is now a very simple adjustment to make the tangent handrail principle work using CAD.

There is only one difference and the use of a calculator needed.

Instead of using the perimeter of the tangent boxes for going 5. make the circumfrance of going 5 equal a standard going.

Therefore in this instance with a going of 254mm. divide that by Pi to get the radius for going 5.

254 ÷ 3.142 = 80.85mm

10″ ÷ 3.142 = 3 3/16″

So let’s run through the same drawing but using the above radius as going 5.

Part 3a. The new plan view for CAD.

Draw the new plan view with new radius.

Now we have the new radius we can draw the new plan view using this radius.

This will separate the stringer faces by about 34mm 1 3/8″ more but will keep the handrail flowing nicely and at a constant pitch through the turn as down the flight.

Loft the new handrail centre line.

Benefits of using the tangent system and stretchout.

The advantage of using the tangent system and the stretch out is the opportunity to position the newels and spindles, with the staircase stretch out for its development you can position the spindles to make sure the spacing works and to get the heights for turning, this is especially useful when working on cut string stairs and using spindles where the bottom block is of constant height and an adjustment is made to the turn length of the stairs.

A few pictures of 180º wreathing pitch to pitch at “constant pitch through turn” using the tangent handrail system.

A wreathing pitch to pitch with ramps builts in top and bottom to allow for the adjustment in height.

180º p-p front view.
180º p-p front view.
180º p-p underside.
180º p-p underside.
180 p-p side view.
180 p-p side view.

This is a traditional pitch to pitch handrail set over nosing mounted spindles, this was a restoration project we carried out on a late 19th century property.

The handrail just needed a few joints re setting and a refresh and revive to restore it back to its former glory.

The stringers will be offset farther than when the spindles are tread housed; to allow for the constant pitch line to still set over the spindles.

180 p - p restoration front view.
180 p – p restoration front view.
180 p - p restoration oblique view.
180 p – p restoration oblique view.

In this picture the same pitch to pitch angle is used, keeping the pitch through the turn the same as through the flight, with the introduction of an extra tread through the turn the stringer separion is doubled to keep that pitch, therefore a full going is used as the distance between the spindle centre lines.

The handrail in this picture was probably not created by the tangent system as the joint in the centre of the turn is verticle nd not perpendicular to the pitch angle.

This was probably carved by setting blocks onto the ends of the straights and plumbing the lines up from the stringer faces.

When looking closely at the grain in the timber you can see it has not been selected as one would with the tangent system.

So not part of what we are looking at here but shows another option for creating the handrail turns.

180 p-p doble rise not tangent system.
180 p-p double rise not tangent system.


Part 1.

A look at the tangent stretchout.

Part 2 introduction.

The dimensions and layout for the CAD view of drawing tangent handrail using half a going between handrail runs.

Part 2a.

How the tangent handrail stretchout looks when overlaid onto the CAD stretchout of the same floor plan.

Part 2b.

How to adjust the handrail centreline flow to mimic tangent handrailing.