Merging flow and BS 9999

[Revol]

I'm having a quick think about merging flows, given in AD-B and BS 9999 as;

W = ((N/2.5)+(60S))/80

Where N is the number of people entering the stair at ground floor and S is the width of the stair.

I'm interested in the fact that S (the width of the stair) is some what irrelevant given the occupancy capacity of the stair is a derivation of the risk profile rather than the actual width of the stair. For example, a building which has an A2 profile during the day but has some out hours community use in the evening (B2 profile). Each would have exactly the same sized stair, lets say 1200mm wide but the number of persons that it could serve would vary ... A2 profile @ 4.5mm/person = 266 persons, B2 profile @ 4.8mm/person = 250 persons ... so an additional 16 persons. If you then consider N (the flow of persons entering the stair at ground level) for a 800mm clear width, A2 profile @ 3.3 mm/person = 222 persons, B2 profile @ 4.1 mm/person = 195 ... so and additional 27 persons.

In calculation of the final exit size using the formula as stated there is no modification for the fact that under one risk profile and additional 43 persons could be using it. Is it just the case that given the formula is taken from AD-B and therefore the old 2.5 mins, 5mm/person exit unit width that there is enough 'fudge factor' within the calculation?

[wee brian]

There's so much uncertainty in these sums that getting too clever is a bit ridiculous. I've got the original derivation of the formula if you want it.

[Revol]

wee brian ... I think you've correct. It's not a terribly sophisticated calc and as you say there is a lot of uncertainty over the 'interactions' of persons during the merging flow. Yes please on the original derivation

[Phoenix]

Remember that the equation came from ADB where risk profiles do not exist so simply copying it across was bound to produce anomalies.  The formula is daft in a number of ways.

For one thing it has its measurements in metres when all other exit width measurements are in mms, so many people get confused and put the wrong numbers in.  Indeed, if W and S are expressed in mm then the equation becomes

W = 5N + 0.75S

which is a lot easier to calculate and remember.

In your example, Jon, you used different risk profiles at different times of day but what if the stair is shared by different risk profiles at the same time?  This is not uncommon.  What risk profile do we apply to the stairs?

And what if the stairs are larger than the minimum width required for means of escape purposes, for example for aesthetic reasons.  Should we take S to be the required width of the stairs and not the actual width?

And what about this figure N?  How do we know how many of the ground floor population are going to choose to exit that way? 

For example, if the door into the staircase at ground floor level is 820mm wide and the risk profile is B2 then it has a maximum capacity of 200 (!).  Lets suppose that there are 400 people on the ground floor and it has two other exits, one 1800mm wide and the other 1640mm wide.  Now the worst case would be the 1800mm exit being lost so how do we apportion the people between the two available exits?  2:1?  There are a number of ways of doing it.  Maybe, you could say that N = 200 as a worst case scenario so that's the figure that should be used but others might think that you were being rather onerous in doing this. 

The thing is, it's not predictable.  We're trying to predict a chaotic system by means of a simple and precise formula.  This is just not possible so it's bound to be wrong in many ways. 

The best we can hope for is that there is some safety margin incorporated into the formula so that however a chaotic evacuation may actually play out, the calculated exit widths will allow people to evacuate in a safe time. 

I cannot tell you if this is the case for this formula.  If you could let us all in on the derivation of the formula, Brian, that would be very interesting. 

I can tell you that at least some of the exit width figures in BS9999 have been demonstrated to be significantly worse than ADB, though whether or not they are dangerous, only time will tell.

[wee brian]

tada!

Ground floor storey exit and stair sharing a common final exit

Where a ground floor storey exit shares a final exit with a stair via a ground floor lobby, the flow capacity of the final exit should be sufficient that neither the flow of occupants from the ground floor nor the flow down the stars should be inhibited at the final exit.  Three possible solutions to this problem are outlined below, from which one is recommended for consideration

1. One possible solution is to provide the same aggregate exit width as would have been provided had the ground floor storey exit been a final exit separate from the final exit serving the stair.
For this solution:
The final exit should be the sum of the widths of the ground floor storey exit and the width of the stair (as would be the case if they were separate). 
The lobby distance from the foot of the stair or the storey exit to the final exit should be a minimum of two metres to enable the two steams merge and flow efficiently towards the final exit.
Example:
A ground floor storey exit serving 250 persons is 1250 mm
This  shares a common exit with a 1.2 metre stair.   
The final exit is therefore 1450 mm

2. Another possible solution is to consider the ground floor as an additional storey served by the stair.  For a simultaneous stair this would result in the addition of 100 mm or 200 mm to the final exit width, or more if a large ground floor population were served by the storey exit.  For a phased stair it would result in no change unless the number served by the ground floor was larger than that on other floors.  A problem with this possible solution is that with the current guidance in AD B it is likely that some inhibition of both the ground floor and stair flow would occur, since the flow capacity of the final exit would be less than the combined maximum flows through the storey exit and down the stair.   
Example: A ground floor storey exit serving 250 persons is 1250 mm
This shares a common exit with a 1200 mm stair serving 420 persons on 5 floors using a simultaneous evacuation strategy.
The modified situation is for 670 persons served on 6 floors.  The required final exit width is not less than that of a stair designed to serve this number of persons, which is 1700mm

3. It is proposed that the most important requirement is that the flow capacity of the final exit should be not less than the maximum flow rates required for the stair and the ground floor storey exits so that neither flow is impeded by the other. 
This can be achieved by a simple calculation as follows:
Final exit width = Required flow rate capacity/80
Required flow rate capacity of final exit = flow rate from ground floor + flow rate from stair
Where:
Flow rate from ground floor (persons/min) = Number served/2.5 min
Flow rate from stair (persons/min) = Stair width (m) x 60 persons/min/metre
A further proviso is that the final exit width should not be less than the stair width
Example: A ground floor storey exit serving 250 persons is 1250 mm. This shares a common exit with a 1200 mm stair
  Required flow rate capacity of final exit (persons/min) = 250/2.5  + 1.2 x 60
                      = 172
 Required final exit width (mm)             =  1000 * 172/80
                                                                =   2150 mm
It is recommended that the third solutions should be adopted as the simplest and least onerous solution achieving the desired objective of no inhibition of flow from either the ground floor or the stair.

[kurnal]

I think the exit in example 1 should be 2450 mm wee b?

[Phoenix]

Thanks Brian,

Before this equation came along (2006) we used to argue between two main possible solutions that are almost as described in solutions 1 and 2.  However, for solution 2 we would have required the whole staircase to be 1700mm wide and not just the final exit.

So for your example, solution 1 would have had a 1200mm wide staircase with a 2450mm wide final exit and solution 2 would have had a 1700mm wide staircase and 1700mm wide final exit.

This does not appear to be what the author is describing.  Do you know where solution 2, as described in your post, came from?  

[wee brian]

they aren't my sums.

Why would you make the stair bigger because of a merging flow at ground level?

[Phoenix]

Because stairs are not only sized to provide a flow rate, they are also sized to provide a holding capacity.  The objective is to allow the floors to be emptied in the nominal 2.5 minutes.  The merging flow at ground level is bound to cause a slowing of the flow rate down the stairs so, to compensate for this reduced flow rate, the holding capacity of the staircase throughout its height has to be increased.  That's the theory.

Solution 1 doesn't need to increase the size of the stairs because the larger final exit will stop the merging flow from inhibiting flow rate down the stairs.  Again, that's the theory.

None of this theory provides an adequate answer to the original query.

[wee brian]

the answer to the original question, IMHO, is that there is a flow of people coming from the stair which will be proportionate to the width of the stair.
hence "Flow rate from stair (persons/min) = Stair width (m) x 60 persons/min/metre"

so long as you dont impede these people then there's no need to increase the storage capacity of the stair - Thats what the formula is trying to do by adding this flow of people to the flow of people comming through the ground floor storey exit.

Its the fact that people asked for outrageousely wide exits and even stairs that this was introduced.