Our interpretation of this is the measurement of the longer side of the stair slab. The recording of data regarding this variable is very simple, we simply used a measuring tape and measured the distance between one end of the stair to the other end before recording down the data. From there, we then recorded the time taken for four person to run from the different amount of width by assigning a specific spot where there can evacuate down only.
The relationship of the width of stairs to the total time is inversely proportional. This is because when the width increases ,more people would be able to evacuate at a time and therefore the time taken would decrease. As seen in the labels of the graph,
x = Number of people able to fit the width at once
y = Total time (seconds)
This is such that to solve issues when the width of stairs is = 1
The best fit equation would be : y=kx+c therefore
y=0.61/x+6.45 or Evacuation time (t)=0.61/Width of stairs +6.45
This total time is used because we are solely considering the width of staircase to the timing of going down 1 level as the only variable. We will be combing all of the variables in the next sections.
3. FORMULATING A FORMULA
Here is the list of different variables and their relation with the total evacuation timing (t):
y=Total evacuation timing (t)
x=Reaction time (R)
8=Time taken to travel down 1 storey (T)
It can also be written as: t=R+T
Number of storeys
y= Total evacuation time (t)
x=Number of storeys (S)
8=Time taken to travel down 1 storey (T)
It can also be written as: t=T(S)
If we combine what we have so far we will get: t=R+T(S)
* * This is provided we assume that the time taken to travel down 1 storey is at a constant of 8 seconds. We rounded off the results for the first 2 variable so that it is more easy to combine them later. This time to taken to travel down 1 storey is simply an assumption. The value of this time to taken to travel down 1 storey will be answered in the “width of stairs” section. **
Distance between housing and nearest stairs
y=Time taken from housing to stairs (ths)
x=Distance between housing and nearest stairs (D)
It can also be written as: ths=0.51(D)+0.08
If we combine what we have so far we will get: t=R+T(S)+0.51(D)+0.08
Width of stairs
y=Time to go down 1 storey (T)
x=Width of stairs (W)
It can also be written as: T=0.61/W+6.45
With all of the variables collected, we will get:
Since T=0.61/W+6.45, we will get:
To break it down in terms of time, you will get:
R= Reaction time
S(0.61/W+6.45)= Time to travel a given number of stories
(0.51(D)+0.08)= Time to travel from housing to stairs
Technically, in simpler forms, the formula can be broken into,
Total time=Reaction time+Time to travel a given number of stories+Time travel from housing to stairs
This diagram shows a the formula in a pictorial form
We, through this simple idea of the different timing adding up together to give us the total timing (t) we then came out this formula. This is because we have to various formulas of the different relationship have with the time, through this, we can simply combine them.
4. Explanation of mathematical models
As stated above, the effect of each variable of the evacuation time (t) is the following:
1. Reaction time
As stated before, the relationship of the reaction time to the evacuation time (t) is directly proportional. Therefore, as the reaction time goes up, the evacuation time (t) would be affected to and it will increase too. This is because with a longer reaction time, the person would carry out their actions later.
2. Number of stories
As stated before, the relationship of the number of storeys and the evacuation time (t) is directly proportional. Therefore, as the number of stories increases, the evacuation time (t) would increase too. This makes sense since the higher up you live, you would take a longer time to go down.
3. Distance between houses to nearest staircase
As stated before, the relationship of the distance between housing and stairs and the evacuation time (t) is directly proportional. Therefore, the distance between the stairs and houses increases, the evacuation time (t) would increase too. This is because with a longer distance, the residents have to spend a longer time running.
4. Width of stairs
As stated before , the relationship of the width of stairs to the evacuation time (t) is inversely proportional. This is because when the width increases ,more people would be able to fit the stairs and evacuate at a time and therefore the time taken would decrease too.
5. Analysis and conclusion
From our mathematical model, we have came up to some conclusion regarding on how to make the evacuation timing of the residents more efficient. This are the MAIN requirements:
Building should be no taller than 75 storeys (180m) ✓
Through calculations, we have come to a conclusion that HDB buildings should be no taller than 75 storeys/180m. This is because given that during a fire, people would crowd all over the staircase, squeezing together, taking them longer to travel down level by level. By right, this maximum number should be lower since this calculation is if we solely consider it as the only factor. HDB has been fulfilling this requirements, with the highest of their flats being 40 storeys/96m.
The width of stairs should not be any lower than 97.5cm ✓
Through calculations, we have come conclusion that in order of a swift evacuation, the width of stairs should be no shorter than 97.5cm, this is so that we can at least 3 people can evacuate at a time. HDB has been fulfilling this requirement, with most of their flats having a width of stairs of at least 1.3m.
Here are some of the methods which we felt that would help improve the evacuation time even further. We then consider if it was feasible or not:
Adding fire alarm on every level. ✓ (Feasible)
By adding fire alarm on every level, this would decrease the reaction time for residents, thus this would eventually lead to the allocation of more time for evacuation.
By adding more sets of staircase. ✓ (Feasible)
This method is especially effective when it comes to wide buildings where the distance between the house to the stair is a distance away. By adding another set of staircase, this would reduce the time needed to travel from the house to the staircase since the distance is being reduced, it also gives the residents an alternative route in case one of the stairway is inaccessible.
Maximum number of residents in each unit. ✓✗ (Possible)
This would be counted as a rule that no more 10 people should reside in the same unit, especially if these people are not related to each other, unless it has passed through inspection by the HDB. This will make sure that all the people in the building will be able to evacuate and there would not be a human congestion at the staircases.
Performing regular checks for the equipments and obstruction. ✓(Feasible)
This method is especially effective since it helps prevent cases such as obstruction caused by items such as potted plants during a fire. Furthermore, this helps ensure that all the walkways meets the requirements.
In conclusion, HDB has met the MAIN requirements needed for a swift evacuation. However, there might be some ways to improve it such as adding fire alarms on every levels or adding more set of staircase.
6. other references
Singapore Civil Defense Force (2016). Fire Incident Statistics 2016. Retrieved 28 March 2017, from www.scdf.gov.sg%2Fsites%2Fwww.scdf.gov.sg%2Ffiles%2FFire%2520Stats%25202016.pdf
Singapore Civil Defense Force (2005). Fire Incident Statistics 2005. Retrieved 28 March 2017, from www.scdf.gov.sg%2Fcontent%2Fscdf_internet%2Fen%2Fgeneral%2Fnews%2Fstatistics%2F_jcr_content%2Fpar%2Fdownload_12%2Ffile.res%2Ffire_stats_Jan_Dec2005.pdf