John T. Thorngren 
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    Our son, John T. Thorngren, Jr., passed away on 
    January 1, 2017. I strongly believe that his 
    accident on a riserless stairway was a contributing 
    factor to an early death. 

         Slips, trips, and falls are responsible for accidental deaths 
   second only to motor vehicles.  According to OSHA, 15 percent of all
   accidental deaths come from this source, and nationally, 10 percent of
   all injuries. Stair falls account for a large percent of such injuries.
   How can a fall down a stairway be fatal? A few broken bones, perhaps,
   but fatal? The answer -- unfortunately -- occurs from closed head
   injuries and broken necks. If not fatal, star injuries can be quite
	Stair falls can be grouped into three categories: 1. Catching 
   one’s toe between stair steps while ascending (toe-catch), 3. Catching
   one’s heel between stair steps while descending (heel-catch), and
   3. Other means of tripping or losing one’s balance.   This publication
   looks at the first two types of stair falls, the toe-catch and the
   heel-catch.  Three different stair designs in public buildings will be
   investigated.  All three stairways were made of bone-crushing concrete.
   The most dangerous of these designs -- in this author’s opinion -- may
   surprise you.

   RISER       The vertical backing, solid barrier between
               successive stair steps (Fig. 1a).   
   RISERLESS   Those designs which are open between stairs
               and have no solid, vertical barriers (Fig 1b).
   RH          The rise or riser height, the vertical
               distance between the tops of a successive 
               stair steps. 
   RO          The open height or open riser height between
               successive stairs.  Some riserless stairs 
               have a partial solid riser (Fig. 1c). 

   T           The thickness of a stair step.
   TW          The tread width of the stair step measured 
               from its front tip to its rear. If the stair
               has a riser, this distance is measured from
               front tip of the stair to the front side of
               the riser.
   V           The overlap distance from the front tip of
               a step to the rear end of the next step on
               riserless designs, from the front tip of a
               step to the front side of the riser on 
               designs with risers.
   RUN         TW less V

      Local building codes differ but most conform to the
  Uniform Building Code(1)(UBC), specifically the 1997 
  edition. Requirements for stairways are relatively few.
  There are no UBC specifics on riserless dimensions. 
  Those items noted under STAIR TERMINOLOGY are restricted
  in public buildings as follows:
      RH    not less than 4.0 inches nor more than 7.0 
            inches and the greatest RH shall not exceed
            the least on any flight by more than 3/8 inch.

      RUN   not less than 11.0 inches, of uniform size
            and shape except the largest RUN shall not
            exceed the least on any flight by more than
            3/8 inch.


       The human foot is shown in Fig. 2 - Foot Terminology.
  Subscript "f" on the following items refers to the bare 


     B   The ball of the foot, fulcrum point when walking
         or stepping down a set of stairs.
     FC  The fulcrum length measured from the ball to the
         back of the heel.
     HH  The height of the heel measured from its bottom 
         to the break at the vertical rise of the leg.
     CF  The height from the bottom of the heel to the 
         break at the bulge for the calf muscle.
     LN  The indention measured between the leg and the
         vertical line touching the back of the calf and
         the heel. 


      A low-heel shoe more or less conforms to the shape of
  the bare foot. Low-heel shoes pertain to the male (50 %)
  of the population and many female designs and therefore 
  must represent a major portion of heel-catch injuries.
  The shoe is shown as a straight line image in 
  Fig. 3 - Shoe Terminology. 


  Subscript "s" refers to the same items in the previous 
  table. Since a low-heel shoe more or less conforms to
  the shape of the bare foot, the thickness of the shoe 
  material increases the dimensions FCf, HHf, LNf and CFf.
  An approximate average for items chosen for our "standard"
  shoe become:

                FCs = 8.0  inches
                HHs = 3.25
                CFs = 9.25
                LNs = 1.5


       Heel-catch is primarily a riserless stair phenomenon.
  Our standard shoe noted previously is superimposed on a
  set of riserless stairs. Only the pertinent dimensions are
  shown, namely LNs, FCs, and RO.


       The shoe forms a triangle noted below at which point 
  the bottom of the heel just catches the underneath front
  edge of the step while descending. 

       This can be mathematically represented as a 
  dimensionless heel-catch number HN given by

        HN   =  [(FCs)2 - (RO)2]/[(FCs - LNs)2]           (1)  

  For HN greater than or equal to 1.00, heel-catch is
  probable. A general notation form this equation is that 
  the greater the value of HN (above 1.0), the greater 
  the probability of injury.  This applies down to a 
  practical point where RO can no longer intercept the 


       Toe-catch is also a riserless stair phenomenon. 
   Toe-catch is probably not as frequent as heel-catch due 
   to the old cliché, "the nature of the beast": one's 
   natural gait pulls the foot away from the open riser 
   area (the jaws of death, so to speak).
       Also toe-catch falls while ascending are probably not
   as devastating as a heel-catch while descending. The 
   victim generally can break his fall and stop sliding
   farther down the steps. During a heel-catch fall, the
   victim frequently tumbles disastrously all the way to
   the landing.


          Figure 6 - Design Number One

  Theses stairs are riserless and are located in an apartment
  complex with the following dimensions in inches:

         RH = 8.25    RO = 5.875    V = 1.125	

  The heel-catch number from Eqn 1 with our standard shoe 

       HN = [(8)2 - (5.875)2]/(8 - 1.5)2 = 0.477 
  Heel-catch is not especially probably with this stairway. 
  Toe-catch falls are probable.

            Figure 7 - Design Number Two

  These stairs are riserless and located in a commercial 
  building, They have been carpeted with a thickly woven
  fabric, an act which although intended to cushion a fall
  actually decreases riser opening, RO, and effective stair
  width, RUN. These stairs have the  following  carpeted 
  dimensions in inches:

	RH  =  6.625      	RO = 3.875       V = 2.75

  The heel-catch number with our standard shoe becomes 1.16
  and heel-catch falls are probable.  Because of the small RO, toe-catch falls are 
  more probable for this riserless design than that for Design Number One.

            Figure 7 - Design Number Three

  These stairs have solid risers and are located in the 
  parking garage for a hospital well known for treating 
  and rehabilitating closed head injuries. The probability 
  of either a heel-catch or toe-catch fall is not remarkable.
  With respect to heel-catch and toe-catch injuries, these
  are felt to be the safest stairs of all.

      It is the opinion of the author, a registered 
  professional engineer in the state of Texas, that 
  the stair design noted as Stair Design Number Two is 
  most hazardous.  It is further felt that building
  codes for public buildings should not allow riserless
  stairs on all new construction and should outlaw
  and rescind grandfathering of any riserless stair
  whose  riser opening is less than 5.50 inches.

      This analysis is dedicated to my son, John T.
  Thorngren, Jr., who suffered a near fatal accident 
  on Stair Design Number Two.  Our family expresses 
  their thanks to Parkland Hospital, Dallas, for life
  saving measures and to Kindred Hospital, Dallas, 
  for excellent direction on a long voyage to 

  1. 1997 UNIFORM BUILDING CODE Vol. 1, International 
     Conference of Building Officials, 5360 Workman
     Mill Rd, Whittier, CA 90601, ISBN 1-884590-87-X,

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