Summary: This post looks at the time tested Minnesota DNR references for ice cream thickness for different recreational tasks and compare them with three papers on the subject. Some of the recommended formulas for hefty loads on properly kept ice roads are substantially less conservative 보다 the MN DNR numbers and are not suitable for to chat activities. NOTE: ice cream thickness is simply one element in the stamin of an ice sheet. In particular, ice can weaken conveniently in thaw conditions. V the fast warming that the arctic and also sub-arctic there were 18 fatalities in Alaska and Northern Canada in the 2019 ice cream season. In the ahead 7 years there were, top top average, much less than one accident every season from these regions. There are also all species of weak clues that can be found on ice. Press ridges and especially urgent ridges are plentiful, essentially on larger lakes. Urgently ridges have the right to be hard to see. Holes of various types are periodically common. This is defined on the Ice perils section.
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Detail: The beginning of the Minnesota DNR references is not clear, however, whoever arisen them did so in a reasonable fashion. Tim Smalley, their recently retired water safety and security specialist, and also his team have actually done and also continue to carry out a particularly an excellent job of comes up with handy advice ~ above recreational ice cream use. Their work has actually been widely adopted by other states and towns throughout the ice cream belt. Your website is fine worth a visit.
Ice roads in the good White North
Ice roadways are the best means to haul tons in parts of Canada. There has been a lot of work done towards making ice roads safer. Plenty of papers have been written on various elements of this problem. The three papers debated here are:Use of ice cream Covers because that Transportation by L. W. Gold, published in 1971. Gold"s occupational is based largely on empirical data of what did or did not autumn through and also the ice conditions involved. His reports are the communication for lot of the work-related that followed. His argued formula for thickness if some danger was acceptable, provides values that are at or listed below the breakthrough thickness because that weights connected with to chat activities.BEST exercise for Building and also Working for sure on ice Covers in Alberta This paper is an excellent look at working on ice. That offers straightforward advice for recreational activities.
The toughness of a cold, black color ice sheet boosts with the square the the thickness: 2" ice will certainly support four times an ext load 보다 1" ice, every other components being equal.
The an easy formula is:
P=Ah2 This is periodically referred to as "Gold"s Formula".
Another type is:
WhereP is the loadh is the thickness the the ice sheetA is a continuous which has actually units favor pounds every square inch (psi), tons/square inch, kg/cm2 or pascals (newtons/ square meter). Because that this discussion we will use devices of pounds and also inches. The numeric value of A can quickly be convert to various units. C is a proportionality continuous between flexural strength and bearing strengthF is the flexural toughness as measured in simple beam tests with the peak in tension
In CRREL Report 78-9: Flexural strength of ice cream in temperate lakes the authors (A.J. Gow, H.T Ueda and also J.A.Ricard) found listed below freezing ice strengths ranging from 130 to 230 psi (average 180 psi). Based upon their work they concluded the the proportionality consistent (C) is about 1, meaning C*F=F=A therefore "A" is a reasonable calculation of the flexural toughness of ice together they measured that on post Pond and also Cannan Street Lake in new Hampshire. This renders it simple to calculation bearing strength from flexural toughness which is relatively easy to measure.
Their report likewise includes a few tests in heat conditions. They discovered strengths as low as 50 psi. We have actually measured much lower values in advanced thaw problems (see "Stage 5" top top the thawed Icepage). Thawing ice cream is much an ext variable and harder to assess. This is an especially true with at an early stage season warmth spells that occur while the ice is tho thin. Much thicker ice in the spring often masks its low details strength. Thin brand-new ice in the feather is especially vulnerable to the solid spring sun. Ice cream in the 2 to 3 inch variety can substantially weaken in a couple hours or much less of sunny conditions.
Note: an example of strong ice I have tested to be 286 psi native a single crystal that S1 ice. The ice sheet it remained in was fine thawed with a flexual stamin in adjacent S2 ice cream (small decision size) was abouit 50 psi. A check of cold eye ice that had actually been through some thaw cycles experiment at 280 psi (Lake Willoughby 2017). The measurement apprehension is at the very least 5%.
Safety Factor: ice sheets have several typical features that reduce their strength. Examples include wet cracks, changes in thickness, locations that froze later than what you room presently standing on, etc. Snow drifts have the right to inhibit ice growth and also reef currents, gas holes, etc can thin the ice cream from underneath. Also the load you i have loaded on an ice sheet could change really quickly if three friends skate as much as you because that a conversation. The safety factor is an effort to reduce the hazard that any kind of areas the weaker ice are below the breakthrough strength. A safety element of 3 is usual for recreational ice use. This appears to be sufficient for people who space well ready for dealing with falling through.
A formula because that safety element is: Safety variable (S) = the typical body load breakthrough strength of cold ice cream (150 psi) divided by the pack (lbs) times the thickness squared (hxh, in inches).
Note: as soon as using this formula a safety aspect of "1" is the breakthrough thickness. Obviously you can"t have a security factor listed below the breakthrough force.
Thaw weakened ice cream is clearly excluded in most minimum thickness recommendations. The is usual to one of two people not acknowledge that ice cream is being weakened through thawing or to no care. Although many civilization get away with it, that is pushing your luck. Reasonably well thawed black ice (stage 4) has actually a toughness of about 50 psi (1/3 that the 150 psi that represents the typical strength of cold ice).
Body load Breakthrough: In vermouth we have developed that the 180 lb breakthrough thickness for black ice is around 1.1". This corresponds to a flexural toughness of about 150 psi. Breakthrough strength in this weight selection is clear what skaters and fishermen (on foot) care about most. In a current conversation through Tony Gow he argued using utilizing A=50 psi. This offers a cold ice cream safety element of around three.
With this in mind, Table 1 looks at the Minnesota DNR thickness recommendations.
Ice roadway operators can obtain away through much greater values that "A" together they have countless rules and also procedures because that building, assessing and also maintaining their roads. Worths up of up 250 psi have actually been argued if some danger of breaking v is agree (eg military transport).
Some that the standard are:Non-moving tons need more ice than relocating loadsThere is a selection of agree speeds end the ice. Ice have the right to be considerably weakened by tons moving in ~ the the wrong speed.Snow ice is consisted of at 1/2 the thickness in part studies. This shows up to come from research studies done in Russia prior to 1956. (See discussion suggest 4 below)Sudden and large decreases in waiting temperature warrant an ext conservative "A" worths or a "stay turn off the ice for a day" recommendation. Heat weather is the behind numerous ice fatalities. Wet cracks room treated as reducing the bearing strength by 1/2 at the sheet of the crack because that perpendicular cracks and 1/4 the stamin for cracks parallel to the direction the travel and also next come the vehicle. Layered ice cream (frozen eye ice over slush over black color ice): only the strongest layer is considered.Ice roadway construction, monitoring and also maintenance: The Alberta report go into substantial detail around building and managing ice cream roads. Doing this well has actually a lot of to execute with just how reliable the road will be.
Table 2 perform looks at the assorted recommendations for minimum ice thickness essential to support a 200 lb person on foot. The "Alberta" and also "Gold" numbers room calculated through their ice roadway formulas. Castle are included here to show why they have to not be supplied for to chat activities. The safety variable is based upon the about 150 psi flexural toughness we uncovered in ours body load breakthrough tests.
Note: utilizing this formula a safety aspect of 1 is the breakthrough thickness.
Reference links and also comments:
Ref D: article on Body load Breakthrough Thickness.
Ref G: usage of ice cream Covers for Transportation through L. W. Gold, released in 1971. This document is terrific and widely used perspective on transporting heavy loads over ice sheets in Canada. The numbers 50 and 250 in Table 1 describe values the "A" (in psi). Gold uncovered in his surveys the there to be very couple of breakthroughs below 50 psi and also that, if some hazard was acceptable, the 250 psi to be OK, at least at the hefty loads/thick/cold ice situation that he was most concentrated on. As you can see above, utilizing 250 psi in ~ body load is pretty lot a insurance of a swim.
Gold"s 1960 Paper. This paper has more detail top top the circumstances involved in various breakthroughs and safe passages.
Ref A: BEST exercise for Building and also Working safely on ice Covers in Alberta This is a modern, comprehensive look at practical bearing strength. The number 4 and 7 space values that "A" in units of kg/cm2. Table 3 below looks at their number 14 and TABLE 5: MINIMUM ice THICKNESS because that LIGHTER LOADS. These numbers may look conservative yet for foot take trip it is typical to have two or an ext people stand near each other. Because that snowmobiles, the 7" minimum is concervative yet reasonable.
1) The Minnesota DNR proposal 4" as the minimum ice cream thickness for any kind of ice activity. Ice cream thinner than 4" is an ext likely to have actually thin spots or weak ice. That is especially important that human being going out on ice between 2" and 4" special be proficient with lake ice, be fitted for assessing the ice and also be fully prepared to loss through and rescue themselves and each various other if lock misjudge the situation.
2) many recreational breakthroughs occur at neighborhood thin or weak (thawed) spots that deserve to be discovered on nearly any ice cream sheet (mostly press ridges, freshly frozen open water and also holes of miscellaneous types). Knowing the ice sheet thickness is just a beginning point. Identifying and avoiding thin/weak ice cream is the bigger component of remaining on top. Even much more important is gift equipped and also skilled in ~ rescue the yourself and also others: ice cream claws, check pole/drill, life jacket, throw rope, buddies to through their rope to you, knowledge about escaping indigenous a sinking vehicle or truck, etc.
3) nobody of this recommended thickness numbers apply in thaw problems (see keep in mind above).
4) eye ice in numerous papers top top bearing strength is rated at fifty percent the stamin of black color ice. In CRREL Report 78-9 they discovered cold, fully saturated snow ice come be more powerful than black ice. Snow ice can weaken dramatically in thaw conditions, probably faster than small grain ice. The authors of CR 78-9 suggest that the half strength consideration may make feeling in warm conditions.
5) contradictory to often stated advice top top the www, old ice cream is usually not significantly weaker than new ice if the ice type, level of thaw and also other factors are the same. This might be a situation of writers of advice confuse "old ice" with "thawed ice".
6) If you are thinking of control anything top top ice, save in mind the this is a high risk endeavor. In Minnesota native 1976 come 2013 vehicles account for 60% the fatalities (70% in the early part of the season). Read the Vehicles and Ice web page for perspective and suggestions because that maximizing your possibilities of living through a breakthrough. The finest bet is to leaving your vehicle on shore.
Use the Minnesota DNR references as a beginning point because that minimum thicknesses for recreational tasks on ice that is listed below freezing. That course, thicker is better.
If girlfriend would favor a formula, either of this will job-related :
Don"t use the minimum thickness formulas for ice roads for recreational tasks (unless they have actually an "A" worth of 50 psi or less).
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These recommendations perform not apply to ice that is or has recently been exposed to temperatures above freezing. Solid sunlight can weaken ice cream at temperatures a little below freezing and also speed up weakening at over freezing temperatures. This is more pronounced at lower latitudes and also near the end of the ice season.
For a more comprehensive treatment bearing stamin see Ice engineering (by Lennart Fransson) or flow Lake Ice design (Edited by George Ashton). These resources take right into account how focused the pack is, static vs relocating loads, etc.