determine center of gravity
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Determine Center
of Gravity, and
Roll-Over Angles
on Your VehicleWritten 11!"#
$ran% D&
'a%a Daless#(
Ever thought youwere close to rolling
over? Plug in somenumbers and see!
Included with this extensive documentation is a dynamic spreadsheet that can beused to determine your COG and RollOver angles Please read the documentationbelow to understand how the spreadsheet does it"s #ob $ou can download it )*R*
$eel free to use the +ale Of Contents elo, or sim.ly scroll don
to vie the entire document&
%able o& Contents
/ntroduction
Ca.turing Weights and 0easures
%ools 'eeded
mailto:email.id@worldnet.att.net?subject=Your%20COG%20Article%20on%20JA!http://www.jeepaholics.com/citizensband/forum/pop_profile.asp?mode=display&id=539http://www.jeepaholics.com/tech/cog/COGROA.ziphttp://www.jeepaholics.com/tech/cog/COGROA.ziphttp://www.jeepaholics.com/tech/cog/#_Toc535118705http://www.jeepaholics.com/tech/cog/#_Toc535118706http://www.jeepaholics.com/tech/cog/#_Toc535118707http://www.jeepaholics.com/tech/cog/#_Toc535118708http://www.jeepaholics.com/citizensband/forum/pop_profile.asp?mode=display&id=539http://www.jeepaholics.com/tech/cog/COGROA.ziphttp://www.jeepaholics.com/tech/cog/#_Toc535118705http://www.jeepaholics.com/tech/cog/#_Toc535118706http://www.jeepaholics.com/tech/cog/#_Toc535118707http://www.jeepaholics.com/tech/cog/#_Toc535118708mailto:email.id@worldnet.att.net?subject=Your%20COG%20Article%20on%20JA! -
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(easured )alues
Calculated )alues
*EEP +E%,P
O--+C./E (E.+,RE(E'%+
/ength o& 0heelbase /01
0idth o& 0heel %rac2 1ase /%1
-ront .xle 3eight 4 3-5
0EIG3I'G $O,R *EEP
-ront .xle 0eight 0-
Rear .xle 0eight 4 0R5
Rear .xle 0eight (odi&ied 4 0R6
-ront .xle Elevated 4 3-6
Passenger +ide 0eight 4 0P
Calculating the Centers of Gravity
789 %3E 03EE/1.+E CE'%ER O- GR.)I%$ :01CG;
7$9 %3E 03EE/ %R.C< CE'%ER O- GR.)I%$ :0%CG;
7=9 %3E CE'%ER O- GR.)I%$ 3EIG3% :3%CG;
Roll Over Angles
%3E CG 71./.'CI'G POI'%9
.'.%O($ O- . RO// O)ER
C./C,/.%I'G RO// O)ER .'G/E+
+ide Roll Over .ngle 0.R'I'G!!!
>river +ide Roll Over .ngle 7>+RO.9
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Passenger +ide Roll Over .ngle 7P+RO.9
Rearward Roll Over .ngle 7R0RO.9
-orward Roll Over .ngle 7-0RO.9
+,((.R$ O- RO// O)ER .'G/E+
+uning your ee.2s Roll Over Angles
GR.)I%$ +,PPOR% +%R,C%,RE
/engthen the 0heel 1ase or 0iden the 0heel %rac2
0EIG3% %,'I'G
Redistribute Physical 0eight
/ower the Physical /ocation o& 0eight
Remove ,nneeded 0eight
.pply or Remove Cantilevered 0eight
ROA Alarm 3ystem
0I/+O' I'+%R,(E'%+
C of G ROA 3.readsheet
Wor%sheets
(easured )alues
Calculated )alues
Roll Over .ngles
Addendum4 3econd *dition
-ORCE .'> I%+ E--EC%+ O' O,R *EEP+
0hat is a &orce?
>escribing -orce
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0hy all the emphasis on this?
-ORCE >E+CRIP%IO'+
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/ntroduction
+o o&ten in our trail side conversations we tal2 about the CG :Center o& Gravity; o&one *eep being higher or lower than the CG o& another *eep and we relate this notonly to the ability to get up or down a slope but also to the dreaded thought o&rolling over
$et most o& us have never really &igured out where the Center o& Gravity isactually located on our own *eep and similarly what the Rollover .ngles are
0hy haven@t we done this? 0ell to be honest probably because it isn@t so easy todo
%his writeup is an e&&ort to provide a process that most &ol2s can &ollow todetermine with a reasonable degree o& accuracy the Center o& Gravity and
Rollover .ngles &or their own *eep
%here is some mathematics involved here .lgebra Geometry and %rigonometry
3owever i& you are li2e me and not a math wiA 2id don@t let that scare you away I
have automated all the math via an Excel spreadsheet
.ll that is really reBuired is that you &ollow some simple directions ta2e someaccurate weight and distance measurements and then #ust plug the numbers intothe spreadsheet
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I& you hang in here with me and &ollow this process through you will be rewardedwith the locations o& the &ollowing values &or your *eep
%he D>imensional +ingle Point Center o& Gravity o& your *eep as well asthe
0heelbase Center o& Gravity
0heel %rac2 Center o& Gravity
3eight o& the Center o& Gravity
Roll Over .ngles in &our directions
>river +ide
Passenger +ide
-ront
Rear
I& you can use a tape measure get a &ew minutes access to a truc2 7weighing scale9and you can type some numbers into a spreadsheet you can do this
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Ca.turing Weights and 0easures
In this section you will ta2e some speci&ic measurements o& your *eep &ollowingthese three process steps
Preparing your *eep &or o&&road use
(easuring lengths and heights in your driveway
(easuring weights at a truc2 stop scale
+ools 5eeded
$ou will need the &ollowing tools
%ape (easure
.ccess to a truc2 weighing scale &or approximately F minutes
. means to elevate the &ront tires o& your *eep at least 6 inches o&& theground :Ramps bloc2s a trailer with car ramps on it etc;
. 3elper
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0easured Values
>uring this process you will measure and record the values shown in the tablebelow Each will be explained in detail within this document
Please note I have put &ictitious numbers in this table to use in the examplesthroughout this document $ou will need to record your own *eep@s data in thistable &or use in the &ormulas and spreadsheet I have provided a blan2 table atthe end o& this document &or you to use &or this
6ael Value Descri.tion of 0easured Values
6engths
/01 HF in /ength o& the 0heelbase :.xle center to axlecenter;
/%1 F in 0idth o& the %rac2 :Outer tire edge to outertire edge;
)eights
3-5 5J in 3eight o& -ront .xle 3ub :center;&rom the levelground
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3-6 6J in 3eight o& -ront .xle 3ub :center;&rom groundwhile -ront is Elevated
Weights
0- 6KK 0eight on -ront .xle with *eep /evel
0P 65KK 0eight on Passenger side
0R5 66KK 0eight on Rear .xle with *eep /evel
0R6 65F 0eight on Rear .xle when -ront is Elevated
Convert any &ractions to decimal values -or example a wheelbase measurement o&H6 and FL5inchs would be converted to H6D56F inches /01 M H6D56F
3ere is a table to assist you in converting &ractions to decimal &ormat
$ractions to Decimal Conversion Chart
7 $ractions of an /nch 7 Decimal
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5L5 "&"8#9
5LN 6L5 "&1#9"
DL5 "&1:;9
5L 6LN L5 """
FL5 "&!1#9
DLN L5 "&!;9"
JL5 "&
5L6 6L LN NL5 "&9"""
HL5 "&98#9
FLN 5KL5 "&8#9"
55L5 "&8:;9
DL LN 56L5 "&;9""
5DL5 "&:1#9
JLN 5L5 "&:;9"
5FL5 "&=!;9
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Calculated Values
,sing the data values you recorded above the &ollowing values will be calculatedand used in your e&&orts to determine the Center o& Gravity and Rollover angles
6ael Value Descri.tion of Calculated Values
Calculated Values
3-d 6FD in >i&&erence between -ront 3ub Elevated and-ront 3ub when /evel :3-d M 3-63-5;
/01n H5FJin
/ength o& wheelbase when &ront is elevated
:/01nM+R% :/0163-d6;
0Rd 65F lbs 0eight added to rear axle when &ront axle was
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elevated :0Rd M 0R6 4 0R5;
0t NKK %otal 0eight o& your *eep
:0t M 0- Q 0R5;
I& you would li2e you can calculate these values yoursel& I have provided a blan2table &or you to record these values in at the end o& this document 3owever theExcel spreadsheet will per&orm this &or you automagically!
1ee. 3etu.
1e&ore you begin to ma2e any measurements you will need to set your *eep up #ust
as i& you were ready to ta2e it o&& road %his setup vital to accurately determinethe O&&Road Center o& Gravity and Roll Over .ngles o& your *eep
Please do not s2ip this step
0hatever you do to prepare your *eep &or an o&& road trip do the same now
Pac2 that toolbox spare parts 3i/i&t *ac2 and anything else that you wouldnormally bring (a2e sure everything is sa&ely anchored down
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I& you have two sets o& tires one &or the street and another set &or o&& road putthe o&& road tires on and air them down to the level you would use o&& road
-ill your gas tan2
I& you would normally o&& road with someone in the passenger seat or any otherseats &or that matter ma2e sure this &ol2s are available to 2eep these seats warmwhen you are ta2ing the weight measurements
I cannot overemphasiAe the importance o& weight and weight distribution in and onyour *eep to accurately determine the Center o& Gravity $our e&&orts in settingyour *eep up now will be rewarded in accuracy later
Off-3cale 0easurements
%hese measurements should be ta2en away &rom the weight scale so the scale isnot tied up when it isn@t necessary
0ith a &riend measure and record the &ollowing values
6ength of Wheelase- 6W>
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(easure your *eep@s wheelbase length while it is sitting on level ground and &ullyprepared &or an o&& road trip
$our *eep@s wheelbase is the distance between the centers o& the &ront tire&ootprint on the ground and the rear tire &ootprint on the ground %his is a bitdi&&icult to measure accurately however we can get it by measuring the distancebetween the axle hubs
0ith a &riend measure the distance between the center o& the &ront axle hub andthe center o& the rear axle hub %his will be eBual to the length o& your *eep@swheelbase
(a2e all measurements accurate to a 5L5 o& an inch
3ere is a drawing o& what you will need to measure to capture the wheelbaselength
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Remember to convert &ractions to decimal values
Width of Wheel +rac% >ase- 6+>
(easure the distance between the outer edges o& your rear tires %his is the%rac2 0idth o& your *eep Convert any &ractions to decimal values and record thismeasurement in inches as /%1
3ere is a drawing o& the measurement you need to ta2e
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$ront A?le )eight@ )$1
(easure the distance &rom the center o& your &ront hub to the ground and recordthis as 3-5
1e sure your *eep is sitting on level ground when you do this
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Weighing Your 1ee.
>rive your *eep over to the local &riendly neighborhood weigh station
1e sure to bring whatever means you will use to elevate the &ront axle with youand remember to ta2e whatever this is out o& your *eep be&ore you weigh your*eep
.lso remember to put those other warm bodies in their seats be&ore you ta2e anyweight measurement %his includes you too!
otential 3cale 6ocations
(a#or %ruc2 +tops
3ighway Roadside 0eigh +tations
.gricultural Centers :1ul2 Grain +ales;
+alvage $ards
Recycling Centers
%he scale you choose should be accurate to at least F lbs :5 lb would be better;
Once you have identi&ied the scale you would li2e to use I have &ound it help&ul topay a visit to the &riendly scale operator ahead o& time Explain what you want to
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do and how you will do it 1e nice and be &riendly! (aybe even entice the operatorwith a seat in your *eep &or next wee2ends trail ride
I& all else &ails try 5K!
$our ob#ective is to get &ive to ten minutes on that scale!!!
O
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Rear A?le Weight @ WR1
0eigh the rear axle o& your *eep by pulling the &ront tires o&& the scale plate andrecord this weight as 0R5
Rear A?le Weight 0odified @ WR#
$ou must come up with a means to li&t the &ront axle o& your *eep y the tire.atches at least 6inches higher than on level ground
>O 'O% ,+E . *.C< to do this $ou (,+% elevate your &ront axle >Y +)* +/R*A+C)*3or the geometry will be thrown o&& and your calculation will be &lawed%his is truly vital to the success o& this process
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%he &irst time I did this I used a set o& 5Dinch tall car ramps bolted to 56inchsBuare railroad ties $es this was a pain to carry there and bac2 but it allowed meto li&t the &ront by the tire patches a little more than 6 inches
%he second time I did this a &riend volunteered the use o& a &lat bed trailer
0ith the trailer par2ed in &ront o& the scale plate I put the trailer ramps downand my car ramps on top o& the trailer bed I drove my *eep up and managed toget more than DK inches o& li&t above level this way
OY+)* +/R* A+C)*3yet?
Good now weigh the rear axle with the &ront elevated :at least 6 inches; andrecord this weight as 0R6
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$ront A?le *levated @ )$#
(easure the distance &rom the ground to the center o& the elevated &ront hub andrecord this distance as 3-6
assenger 3ide Weight @ W
0eigh the passenger side o& your *eep by pulling only the passenger side tires onthe scale plate Record this weight as 0P
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$ou have now &inished collecting all the data you will need to determine your *eep@sCenter o& Gravity and Rollover .ngles .ll that is le&t is to do is calculate a &ew&ormulas
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Calculating the Centers of Gravity
B +he Wheelase Center of Gravity 'W>CG(
%he easiest Center o& Gravity coordinate to &ind is where the Center o& Gravitylies relative to your *eep@s wheelbase
%he weight on your *eep@s &ront and rear axles is directly proportional to thelocation o& the Center o& Gravity along your *eep@s wheelbase In &act it is a
direct inverse ratio
%hin2 about it
I& 5KKS o& the weight o& your *eep was located on the &ront axle the Center o&Gravity would be located =ERO inches or KS o& the wheelbase distance &rom the
&ront axle
I& the weight were distributed KS on the &ront axle then the Center o& Gravitywould be located KS o& the wheelbase distance &rom the &ront axle
%o calculate your *eep@sW>CG
:0heelbase Center o& Gravity; you will use thedata values you measured and recorded earlier
Once again please remember I am using &ictitious data in these examples $ou willneed to substitute your measurements or type them into the spreadsheet
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6W>M HF inches M 0heelbase in Inches
W$M 6KK lbs M 0eight on -ront .xle
WtM NKK lbs M %otal weight o& *eep
%he &ollowing &ormula will enable you to determine in inches where the W>CGislocated behind your *eep@s &ront axle
'1 - 'W$ Wt(( 7 6W> E W>CGlocation in inches behind the &ront axle
:5 :6KK L NKK;; HF M
:5 KF5J; HF M
K HF M
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BY +he Wheel +rac% Center of Gravity 'W+CG(
%he location o& your *eep@s W+CG:0heel %rac2 Center o& Gravity; is calculated inmuch the same way as you #ust calculated the 01CG
%he 0%CG coordinate location is a direct inverse ratio o& the weight on each sideo& your *eep to the wheel trac2
3ere are the data elements you will need to use &or this &ormula
6+>M F inches 0idth o& your wheel trac2
WM 65KK lbs 4 0eight on passenger side o& your *eep
WtM NKK lbs 4 %otal weight o& your *eep
%he &ollowing &ormula will enable you to determine in inches where the W+CGislocated &rom the outer tire edge on the passenger side o& your *eep
+ubstitute the data values you measured and recorded and then simpli&y and solvethe &ormula as in this example
'1 - 'W Wt(( 7 6+> E W+CGin inches &rom the passenger side tireedge
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:5 :65KK L NKK;; F M
:5 KDJF; F M
KF6F F M !8&98 /nches from the .assenger side outer tire edge
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BF +he Center of Gravity )eight ')+CG(
%he 3eight o& your *eep@s Center o& Gravity :)+CG; is not Buite as easy todetermine
Calculating the 3%CG is a bit more di&&icult to accomplish It@s di&&icult &or somepeople to even visualiAe and di&&icult &or me to explain
/et me give it a shot
0hen you went about measuring and weighing your *eep one o& the things you didwas li&t the &ront axle :at least 6 inches higher than it would be on level ground;and then you weighed the rear axle
0hen you li&ted the &ront you in e&&ect shortened the wheelbase as it relates togravity In other words the horiAontal distance between the &ront and rear tirepatches became shorter than what it is on level ground
3ere is a drawing that might help in understanding this
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'ow i& we can measure how high we li&ted the &ront axle calculate the length o&this shortened wheelbase and determine how much weight was added to the rearaxle when we li&ted the &ront we will be able to calculate the 3eight o& your*eep@s Center o& Gravity :3%CG;
3ere are three &ormulas you must solve be&ore you can get to the 3%CG
)$d E )$# - )$1M 3eight di&&erence between &ront axle level and elevated
3-d M 6J 4 5J
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)$d E#9&! inches
6W>nE3R+ '6W>H# - )$dH#(M /ength o& the shortened wheelbase whenelevated
/01nM+R% :HF6 4 6FD6;
/01nM+R% ::HF HF; 4 :6FD 6FD;;
/01nM+R% :HK6F 4 KKH;
/01nM+R% :NDNH5;
6W>nE=1&9; inches
WRd E WR# @ WR1M 0eight added to rear axle
0Rd M 65F 4 66KK
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WRd E #19 ls&
O 7 6W>n( 'Wt 7 )$d(( MYour ee.2s CG )eight
3%CG M 5J Q ::65F HF H5FJ; L :NKK 6FD;;
3%CG M 5J Q :5NJKD5J6 L 565K;
3%CG M 5J Q 5FK
)+CG E !#&:" /nches aove the tire .atches
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Roll Over Angles
+o where are we?
0e now 2now the 8 $ and = coordinates that de&ine the D> Center o& Gravity o&your *eep
In the example I@ve been using the Center o& Gravity is located at a point
DF Inches behind the &ront axle
DF Inches &rom the passenger side outer tire edge and
D6NK Inches above the *eep@s tire patches
Can you see it?
I& you can &ind the single point represented by these three coordinates you can
&ind the Center o& Gravity o& your *eep!
+ome people can visualiAe thisT others li2e mysel& have a harder time o& it
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-or the sa2e o& this discussion let@s #ust say these three coordinates de&ine theCenter o& Gravity as the Radio )olume Control alancing oint
%he Center o& Gravity represents the single point where the average weight o& the*eep is located $ou can thin2 o& this as the 71alancing Point9
I& you could somehow reach the Center o& Gravity with a long pole you couldsupport the *eep &rom that pole and rotate the *eep in any direction DKdegrees in D> and the *eep would not &all
-ortunately &or us we do not have to support our *eep@s Center o& Gravity &rom apole nor do we want to balance it in a DKdegree sphere 0e do however balance
itT we do this under normal conditions by balancing the Center o& Gravity on ourtire patches
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I& you were to loo2 at the location o& your *eep@s Center o& Gravity &rom the topyou would see that it &alls within the rectangular support structure &ormed by yourtires on the ground
3ere@s a drawing that might help you visualiAe this
%his is goodness! %his is a stable condition!
'otice that the Center o& Gravity is located within the 7Physical Geometry9 o& all&our tires even though it is not centered It is located at the 8 and $ coordinateswhich you calculated
:In all li2elihood your *eep@s Center o& Gravity will not be centered either;
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.nother way to loo2 at this is that the Center o& Gravity :under normal conditions;is being balanced on top o& a pyramid :instead o& a pole; with the Center o& Gravity
at the apex o& &our uneBual sides
%a2e a loo2 at this topview drawing Perhaps it will help you to visualiAe this
.s long as your *eep@s Center o& Gravity is contained within the gravity supportstructure :Gravitational Geometry; &ormed by the tires your *eep will not roll
I& your *eep@s Center o& Gravity is allowed to move outside the gravity supportstructure &ormed by your tires your *eep will roll!
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%his is a basic law o& physics
Anatomy of a Roll Over
I& you position your *eep in such a way that the Center o& Gravity is moved outsidethe gravity support structure o& your tires your *eep will become unstable and willroll
/ets loo2 at this &rom another view &rom the rear
0hen your *eep is on level ground loo2ing &rom the bac2 the Center o& Gravity iscontained between the driver and passenger side tires or in other words withinthe gravitational support structure
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.s your *eep is positioned somewhat o&&camber to the driver@s side the Centero& Gravity :CG; will move closer to the edge o& the gravitational support structure
:green line;
'ote that the Center o& Gravity did 'O% (O)E in relation to the *eep itsel& :Itis still the Radio )olume Control
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0hy do we roll?
0e roll because the Center o& Gravity is no longer balanced under our 7pre&erredgravity support structure9 &ormed by our tires!
%his is a basic law o& Physics
%he Center o& Gravity is always balanced :contained; within the gravitationalgeometry o& some support structure
I& the Center o& Gravity is moved outside one structure :your tires; the Center o&Gravity will be supported by another support structure :/i2e the side o& your*eep!;
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3ere is what this loo2s li2e &or a rearward roll over
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+imilar drawings &or a passenger side roll over and a &orward direction roll overcould be drawn but I@m tired I@m sure you get it visualiAe these as well
.s you now 2now the Center o& Gravity can be moved outside the gravitationalgeometry o& the support structure &ormed by the tires 0hen this happens the*eep will roll
1ut when will this happen?
%his will happen at a certain angle in each o& &our directions based on the locationo& your *eep@s Center o& Gravity
3ere@s how to calculate these angles &or your *eep
Calculating Roll Over Angles
I& you have done the wor2 to determine where the Center o& Gravity is located &oryour *eep you have all the in&ormation you need to calculate your &our roll overangles
3ere are the data elements you will be using
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ReJuired Data *lements to Determine Roll Over Angles
6ael Value Descri.tion of Data *lement for Roll Over Angles
/01 HF in /ength o& the 0heelbase :.xle center to axle center;
/%1 F in 0idth o& the %rac2 :Outer tire edge to outer tire
edge;
01CG DF 0heel 1ase Center o& Gravity behind -ront .xle M
:5 :0- L 0t;; /01 M 01CG
0%CG DF 0heel %rac2 Center o& Gravity &rom the passengerside outer tire edge M :5 :0P L 0t;; /%1 M 0%CG
3%CG D6NK $our *eep@s CG 3eight M
3-5 Q ::0Rd /01 /01n; L :0t 3-d;; M 3%CG
Please note the &ormulas that &ollow contain the trigonometry &unction o& .rc%angent which presents a solution in 7Radians9 :$es radians are totally useless inthe *eep@n world unless you@re a roc2et scientist;
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Radians are then converted into 7>egrees9 :I understand degrees!; through the useo& a published standard mathematics table
1oth .rc %angents and Radian to >egree Conversions are outside my ability toexplain in this document
%his is the only time I will as2 &or your &aith without an adeBuate explanation'ewton Galileo and Einstein have all proved this &unctions out %hat@s good enough&or me I hope it is good enough &or you as well
$ou can per&orm these calculations on most good scienti&ic calculators or you canuse the Excel spreadsheet I will provide to do this math automagically &or you
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3ide Roll Over Angle - WAR5/5GKKK
.s stated at the top o& this writeup this process will help you determine theCenter o& Gravity and Roll Over .ngles &or your *eep 7with a reasonable degree o&accuracy9
%hat is true however I need to ma2e you aware o& a particular o&&road conditionand it@s potential e&&ects on +ide Roll Over .ngles
%his is important because it is 'O% .>>>RE++E> in these &ormulas
In truth I do not 2now how to calculate these variables
I do 2now it is prudent to ma2e you aware o& any potential that could >ECRE.+Eyour +ide Roll Over .ngles and present you with a rather unpleasant surprise
6*A3* R*AD +)/3K
+he formulas for Driver and assenger 3ide Roll Over Angles DO 5O+ ta%e
into consideration or calculate the .otential effect of the don-slo.e tires
Brolling, sliding or tuc%ing under the heels
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3ow much your tires may 7tuc29 under the wheels will depend on tire siAe pro&ileair pressure sidewall strength and slope o& the angle
0hen tires 7tuc29 under the wheels two physical events occur
5 %he Physical 0idth o& your *eep@s 0heel %rac2 is shortened
%his in combination with the angle your *eep is on will result in an ,'ECRE.+E in Roll Over .ngle! :%his is 'O% Goodness;
6 %he )ertical 3eight o& your *eep@s Center o& Gravity will be lowered
%his will result in an ,'
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Please note I do not 2now o& any means o& calculating these e&&ects at this time
Perhaps in the near &uture we will
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Driver 3ide Roll Over Angle BD3ROA
0hat we will be determining is how many degrees to the le&t you can ta2e your*eep be&ore the Center o& Gravity pierces the vertical plan o& gravity and extendsoutside the gravitational support structure &ormed by the tires
3ere is a drawing o& what we are going to solve
%he vertical blue line represents the vertical pull o& gravity on your *eep Itintersects the angled pin2 line which runs between the outer edge o& the driver
side tire and the Center o& Gravity o& your *eep
%he angle that is &ormed between these two lines is the >river +ide Roll Over.ngle
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3ere is the &ormula we will use to calculate the D3ROA
D3ROA E D*GR**3 'A+A5 ''6+>@W+CG()+CG((
>+RO. M >EGREE+ :.%.' ::F4DF;LD6NK;;
>+RO. M >EGREE+ :.%.' :6NLD6NK;;
>+RO. M >EGREE+ :.%.' :KNJKJD5;;
>+RO. M
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assenger 3ide Roll Over Angle B3ROA
0hat we will be determining is how many degrees to the right you can ta2e your*eep be&ore the center o& gravity pierces the vertical plan o& gravity and extendsoutside the gravitational support structure o& your tires
3ere is a drawing o& what we are going to solve
%he vertical blue line represents the vertical pull o& gravity on your *eep Itintersects the angled pin2 line which runs between the outer edge o& thepassenger side tire and the Center o& Gravity o& your *eep
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%he angle that is &ormed between these two lines is the Passenger +ide Roll Over.ngle
.nd here is the &ormula we will use to calculate the 3ROA
3ROA E D*GR**3 'A+A5 'W+CG)+CG((
P+RO. M >EGREE+ :.%.' :DFLD6NK;
P+RO. M >EGREE+ :.%.' :555D5;
P+RO. M
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Rearard Roll Over Angle BRWROA
0hat we will be determining is how many degrees to the rear you can ta2e your*eep be&ore the center o& gravity pierces the vertical plan o& gravity and extendsoutside the gravitational support structure &ormed by the tires
3ere is a drawing o& what we are going to solve
%he vertical blue line represents the vertical pull o& gravity on your *eep It
intersects the angled pin2 line which runs between the centerline o& the rear tirepatch and the Center o& Gravity o& your *eep
%he angle that is &ormed between these two lines is the Rearward Roll Over .ngle
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.nd here is the &ormula we will use to calculate the RWROA
RWROA E D*GR**3 'A+A5 ''6W>@W>CG()+CG((
R0RO. M >EGREE+ :.%.' ::HF4DF;LD6NK;;
R0RO. M >EGREE+ :.%.' :F5LD6NK;;
R0RO. M >EGREE+ :.%.' :5FNHK6;;
R0RO. M 9;&ac%ard E Rearard Roll Over Angle
$orard Roll Over Angle B$WROA
0hat we will be determining is how many degrees to the &ront you can ta2e your*eep be&ore the center o& gravity pierces the vertical plan o& gravity and extendsoutside the gravitational support structure &ormed by the tires
3ere is a drawing o& what we are going to solve
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%he vertical blue line represents the vertical pull o& gravity on your *eep Itintersects the angled pin2 line which runs between the centerline o& the &ront tirepatch and the Center o& Gravity o& your *eep
%he angle that is &ormed between these two lines is the -orward Roll Over .ngle
.nd here is the &ormula we will use to calculate the $WROA
$WROA E D*GR**3 'A+A5 'W>CG)+CG((
-0RO. M >EGREE+ :.%.' :DFLD6NK;;
-0RO. M >EGREE+ :.%.' :5D6JDH;;
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-0RO. M 9!&"1 Degrees $orard E $orard Roll Over Angle
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3ummary of Roll Over Angles
%he Roll Over .ngles we #ust calculated &or our &ictional *eep will loo2 li2e this
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+he )igher the Roll Over Angle the >etterK
%hin2 o& the Roll Over .ngle as a bu&&er the de&ined operating range in all &ourdirections where your *eep will remain stable and unli2ely to roll over
%he greater this range :angle; the more you will be able to 7sa&ely conBuer9 in your
*eep
Can you see the relationship between the physical location o& the *eep@s Center o&Gravity and the *eep@s gravitational support structure :tire patches;?
+he greater the horiLontal distance eteen your ee.2s Center of
Gravity and the tire .atch, the greater the Roll Over angle ill e&
Chec2 it out in the drawing above
Can you see the relationship between the 3eight o& the Center o& Gravity and eachRoll Over .ngle?
+he loer you can get your ee.2s Center of Gravity to the ground, the
greater all of your ee.2s Roll Over Angles ill e&
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Conversely i& you raise your *eep@s Center o& Gravity you will decrease all o& your*eep@s Roll Over .ngles
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+uning your ee.2s Roll Over Angles
'ow that you 2now how to calculate the Center o& Gravity and the Roll Over .ngles&or your *eep the Buestion becomes 70hat to do with this in&ormation?9
0ell one thing you can do is 7tune9 your *eep to get the Center o& Gravity and RollOver .ngles more to your li2ing
3ere are a &ew o& the many actions you can ta2e to 7tune9 your *eep@s Center o&Gravity and Roll Over .ngles
/engthen wheelbase andLor wheel trac2
Redistribute Physical 0eight
/ower /ocation o& Physical 0eight
Remove ,nneeded 0eight
.pply or Remove Cantilevered 0eight
Gravity 3u..ort 3tructure
6engthen the Wheel >ase or Widen the Wheel +rac%
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%his action will increase the siAe o& the gravitational support structure on whichthe Center o& Gravity is balanced and increase your *eep@s Roll Over .ngles:Goodness;
/engthening the wheelbase or widening the wheel trac2 is something a2in to puttingoutriggers on a canoe %hey help 2eep it &rom turning over
Weight +uning
%he next &our examples all deal with weight %o best understand these it would behelp&ul to have a general understanding o& the e&&ects o& 7weight placement9 on
your *eep
0here weight is placed along the wheelbase o& your *eep or even outside the
wheelbase o& your *eep will have signi&icant e&&ects on the weight carried by eachaxle %his will a&&ect the location o& the Center o& Gravity and your *eep@s RollOver .ngles
%he closer weight is located to the center o& your *eep@s wheelbase the moreeBually that weight will be distributed on both axles :+ee Green =one in drawingbelow;
.s the weight is moved closer to one o& the axles a higher percentage o& weightwill be placed on that axle and a smaller percentage o& weight will &all over the axle&arthest away :+ee 1lue =ones;
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%hings get real interesting when we hang or cantilever weight beyond your *eep@swheelbase
Cantilevered weight has the most dramatic e&&ect on the weight distribution :+eeRed =ones;
Redistriute hysical Weight
Redistribute physical weight &rom one part o& your *eep to another part
%his will move the Center o& Gravity in the direction you are moving the weight andaway &rom the location where the weight came &rom
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%his will alter Roll Over .ngles :Could be good or not so good;
6oer the hysical 6ocation of Weight
.ny time existing weight can be lowered you will lower the Center o& Gravity o&your *eep
. lower Center o& Gravity will create greater Roll Over .ngles :Goodness;
Remove Mnneeded Weight
Removing unneeded weight will a&&ect the height o& your *eep@s Center o& Gravity
3owever be aware! Removing weight can either raise or lower the height o& your*eeps Center o& Gravity
0eight you remove that was 1E/O0 the original 3eight o& the Center o&Gravity will cause the new Center o& Gravity to rise :%hin2 removing yours2id plates;
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I& the Center o& gravity goes up the Roll Over .ngles will >ecreases :'otgoodness;
0eight that you remove that was .1O)E the originally 3eight o& theCenter o& Gravity will result in a new lower Center o& Gravity :%hin2removing a hard top;
I& the Center o& Gravity goes down the Roll Over .ngles will increase :Goodness!;
A..ly or Remove Cantilevered Weight
$es this is the real interesting weight placement
.ny weight hanging in &ront o& the &ront axle or behind the rear axle is calledcantilevered weight
Cantilevered weight has a 7&orce multiplying9 e&&ect on the weight distributionover your axles and on the location o& your *eep@s Center o& Gravity
%here are two uniBue physical e&&ects o& cantilevered weight
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5 Cantilevered weight will increase the weight on the nearest axle by anamount GRE.%ER than the actual weight being added
6 Cantilevered weight will cause a &ractional >ECRE.+E in the weight on theaxle &arthest away
%he e&&ects o& cantilevered weight on your *eep can be calculated prior to actuallyadding the weight
3ere are the data elements you will need and the &ormulas to calculate the e&&ectso& cantilevered weight
Date *lements ReJuired to Calculate *ffects of Cantilevered Weight
.dd0 0eight o& the ob#ect you are going to place in a cantileveredposition
Cant> %he distance &rom the axle center to the weight you areadding
/01 %he length o& your *eep@s 0heelbase
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In this example we will add a winch and mounting plate to the &ront o& a *eep
AddW E 19" lsM 0eight o& winch and mounting plate
CantD E #8 inchesM >istance to &ront axle center &rom center o& the winchplate
6W> E =9 inchesM /ength o& the *eep@s 0heelbase
3ere is a &ormula that can be used to determine the weight that will be added tothe &ront axle as a result o& mounting a 5FK lbs winch on the &ront bumper
'AddW 7 CantD( 6W> I AddW E Weight added to front a?le
:5FK 6; L HF Q 5FK M
:DHKK L HF; Q 5FK M
5KF Q 5FK M 1=1&"9 ls added to front a?le
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.nd here is the &ormula to determine the how much weight will be removed &romthe rear axle as a result o& mounting this winch on the &ront bumper
'AddW 7 CantD( 6W> E 'Weight removed from Rear A?le(
:5FK 6; L HF M
:DHKK L HF; M
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%he *eep@s 0heelbase Center o& Gravity was also changed It was shi&ted&orward toward the &ront axle by a multiple o& the weight added
I& you care to you can go bac2 and recalculate the new 01CG by adding andsubtracting these weights &rom the &ront bac2 and total o& our example *eep$ou will see that the 0heelbase Center o& Gravity has indeed been moved &orwardas a result o& mounting the winch on the &ront bumper
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ROA Alarm 3ystem
I am in the process o& developing a twoaxis :8 and $; Roll Over .ngle .larm+ystem &or my *eep %his system will monitor the dynamic angles on my *eep andprovide a warning when I am approaching prede&ined Roll Over .ngles
%his e&&ort is currently incomplete
%his RO. .larm +ystem will incorporate the &ollowing design &unctions andattributes
Provide the ability to monitor my *eep@s dynamic angles
Enable the setting o& individual roll over angle 7trigger points9 in degrees in&our directions :/e&t Right -orward 1ac2ward;
Provide an audible alarm when trigger points have been reached
.ll 7trigger points@ will have a built in design error o& 6 to D degrees to
provide a margin o& sa&ety
+ystem must be small :*eep real estate is valuable; and easily mounted andremoved &rom the inside o& my cab
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+ystem must be relatively inexpensive :5KK (ax; and be within thecapabilities o& a reasonably s2illed person to build
Wilson /nstruments
Recently I have become aware o& a patent pending product called ClinoExtremewhich is made by the &ol2s at 0ilson Instruments in +acramento C.
0hile I am still trying to get my hands on one o& these units my &irst and secondglace tells me this may be exactly what I am loo2ing &or I& it is and the cost is
reasonable I will drop my e&&orts to develop my own Roll Over .ngle .larm +ystem
I& you have an interest in learning more about this 0ilson Instruments producthere is their web address
httpLLwwwwilsoninstrumentsm&gcomLclinoextremehtm
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3ere are the highlights o& the ClinoExtreme unit as I understand them
>ual Electronic Clinometers :-rontL1ac2 Pitch and +ide to +ide Roll;
'o moving parts :accept &or the gauge needles;
0arning .ngle .larms programmable by the end user via a R+6D6 computerinter&ace
Cost is un2nown at this time
0hen I get my hands on one o& these units I will let you 2now how it wor2s out &orme
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C of G ROA 3.readsheet
I have a complete Excel spreadsheet titled 7CoGURO.xls9 which will accompanythis writeup
%here are two pages to this spreadsheet titled 7COGRO.9 and 7>ata Collection9
,se the COGRO. page to enter your *eep@s weights and measurement and obtainyour *eep@s Center o& Gravity and Roll Over .ngles
%he 7>ata Collect9 page is optional I am trying to collect data pertaining to thistopic
I am reBuesting that you complete this page and sent the entire spreadsheet to>aless6V$ahoocom
I plan to build an online database that will let you compare your *eep@s CG and RO.to other *eeps in your class
.ll data will be added to the database anonymously
mailto:Daless2@Yahoo.commailto:Daless2@Yahoo.com -
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Wor%sheets
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I have a complete Excel spreadsheet titled 7CoGURO.xls9 which will accompanythis writeup
0easured Values
6ael Value Descri.tion of 0easured Values
6engths
/01 in /ength o& the 0heelbase :.xle center to axlecenter;
/%1 in 0idth o& the %rac2 :Outer tire edge to outertire edge;
)eights
3-5 in 3eight o& -ront .xle 3ub :center;&rom the levelground
3-6 in 3eight o& -ront .xle 3ub :center;&rom groundwhile -ront is Elevated
Weights
0- lbs 0eight on -ront .xle with *eep /evel
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0P lbs 0eight on Passenger side
0R5 lbs 0eight on Rear .xle with *eep /evel
0R6 lbs 0eight on Rear .xle when -ront is Elevated
Calculated Values
6ael Value Descri.tion of Calculated Values
Calculated Values
3-d in >i&&erence between -ront 3ub Elevated and-ront 3ub when /evel :3-d M 3-63-5;
/01n in /ength o& wheelbase when &ront is elevated
:/01nM+R% :/0163-d6;
0Rd lbs 0eight added to rear axle when &ront axle waselevated :0Rd M 0R6 4 0R5;
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0t lbs %otal weight o& *eep
Roll Over Angles
6ael Value Descri.tion of Data *lement for Roll Over Angles
/01 in /ength o& the 0heelbase :.xle center to axle center;
/%1 in 0idth o& the %rac2 :Outer tire edge to outer tireedge;
01CG in 0heel 1ase Center o& Gravity behind -ront .xle M
:5 :0- L 0t;; /01 M 01CG
0%CG in 0heel %rac2 Center o& Gravity &rom the passengerside outer tire edge M :5 :0P L 0t;; /%1 M 0%CG
3%CG in $our *eep@s CG 3eight M
3-5 Q ::0Rd /01 /01n; L :0t 3-d;; M 3%CG
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Addendum4 3econd *dition
$orce and its effects on our 1ee.s
%here will be a 7+econd Edition9 o& this writeup that will &ocus more on exploringthe dynamic e&&ects o& &orce on our *eeps roll over angles as they may occur in theo&& road environment
I thought it might be help&ul here to provide a baseline understanding o& the
&orces o& physics so we could begin to give some thought to which &orces mightapply in what circumstances
Please note that I am not a physicist but rather an interested *eep@r #ust li2e you%his is my attempt to ta2e a complex sub#ect and simpli&y so we may betterunderstand the &orces our *eeps are interacting with and against
What is a forceN
Our *eeps are constantly interacting with many &orces in the o&& roadenvironment 1ut what is a &orce?
. &orce is a push or pull on our *eeps as a result o& an interaction with some otherob#ect say your *eep@s &ront tire against a roc2 or your entire *eep against asigni&icant climb
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0henever there is an interaction between your *eep and another ob#ect there is&orce acting on both
0hen the interaction stops :you ma2e it to the top o& that steep hill climb; your*eep is no longer experiencing the &orce o& the climb
In Physics a &orce only exists as a result o& an interaction between two :or more;ob#ects In the *eeping world a &orce exists as a result o& an interaction betweenour *eep and anything else we encounter on the trail
-orce interactions between your #eep and everything you encounter on the trail canbe put in one o& two categories
Contact -orces
.ctionata>istance -orces
Contact $orces
%hese are the types o& interaction &orces that come into play when your *eep is
physically in contact with another ob#ect
Contact -orces include
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-rictional -orce
%ensional -orce
'ormal -orce
.ir Resistance -orces
.pplied -orce
Action-at-a-Distance $orces
-orces o& this type occur when our *eeps interact with another ob#ect while not inphysical contact with it but are still able to exert a push or pull despite thephysical separation
Examples o& .ctionata>istance -orces include
Gravitational -orces
Electrical -orces
(agnetic -orces
Descriing $orce
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-orce is measured using a standard metric unit 2nown as the 'ewton
'ewton :the one who had the apple &all on his head while sitting under a tree;developed a set o& &ormulas that are used to convert any o& these nine de&ined&orces into a common unit o& measurement %hat unit o& measurement is called a'ewton
%his means Gravitational Pull can be expressed in 'ewtons and -rictional -orce can
also be expressed in 'ewtons .s can the rest o& the &ield
>on@t worryT we@re not going to go here I don@t have anything against 'ewtons:3ec2 I eat them with &igs inside Buite o&ten; 1ut 'ewtons aren@t exactly a parto& my every day vocabulary let alone my *eeping experiences
0e will use more normal words li2e Pounds or P+I or -tL/bs (easures that Ireadily understand without having to calculate an incredible &ormula &or 'ewtons&or 5F minutes and &orgetting why I wanted to 2now the in&ormation in the &irstplace!
Vector uantity for $orce
%here is something we must understand that applies to all &orces and that is the7vector Buantity &or &orce9
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-orces acting on your *eep have a vector Buantity having both magnitude :siAe; anddirection
In order to convey how a &orce is acting on your *eep you must be able to describeboth its magnitude :siAe; and its direction and it is best to do this in a drawing
You cannot say 1" 5etons:0e will use anything but 'ewtons; is a &ulldescription o& the &orce acting on your *eep or a part o& your *eep
You can say1" 5etons, donardsand you would be giving a &ull and completedescription o& a &orce +ee what I am getting at?
1oth the magnitude :5K 'ewtons; and the direction :downwards; are described
1ecause &orce is a vector and it has a magnitude :siAe; and a direction we have toagree on a way to represent &orce in &uture drawings I would li2e to suggest thisapproach It is loosely based on standard called 7&reebody diagrams9 commonlyused in Physics
In our vector diagrams we will use the siAe o& the arrow to re&lect themagnitude or siAe o& a &orce even i& we don@t 2now exactly what that siAeis
%he direction o& the arrows will give the direction in which the &orce isacting
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3ere is an example o& what this will loo2 li2e in the second edition
O&ten one &orce on your *eep is canceled out by another &orce acting on your*eep
In the above drawing KKK lbs o& gravitational pull is canceled out by KKK lbs o&
push &rom the tires In this case two &orces 7balance each other9
1ut &orce can also go unbalanced I& we add a third &orce to the above drawing youwill better be able to visualiAe this
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%he same two 71alancing -orces9 are acting on your *eep and canceling each otherout
0hen a third &orce is now applied in this case an unbalanced &riction &orce astate o& &orward motion exists
$our *eep moves &orward because there is no counterbalancing &orce to stop it!
0ant a counterbalancing &orce? .pply your bra2es! :.ny idea what type o& &orceyour bra2es would be applying? $es you@re right! -rictional!;
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Why all the em.hasis on thisN
0ell you don@t have to have a Ph> in Physics but you do have to &ully understandtwo points in order to understand what &orces are acting on your *eep
(ore than one &orce can be acting on your *eep at any moment in time
.ll &orce has two dimensions (agnitude :siAe; and >irection
I& you understand these two points you have all the tools you need to begin to&igure out what is happening with your *eep in many o&& road situations
$orce Descri.tions
3ere is a short explanation o& seven o& the nine &orces which are most li2ely tocome into play in the *eeping world Please note I pulled this right out o& the boo2
A..lied $orce4
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.n applied &orce is a &orce that is applied to an ob#ect by another ob#ect or by aperson
I& a person is pushing a des2 across the room then there is an applied &orce actingupon the des2 %he applied &orce is the &orce exerted on the des2 by the person
Gravitational $orce4
%he &orce o& gravity is the &orce with which the earth moon or other massivebody attracts an ob#ect towards itsel&
1y de&inition this is the weight o& the ob#ect
.ll ob#ects upon earth experience a &orce o& gravity that is directed WdownwardWtowards the center o& the earth %he &orce o& gravity on an ob#ect on earth isalways eBual to the weight o& the ob#ect
5ormal $orce4
%he normal &orce is the support &orce exerted on an ob#ect that is in contact withanother stable ob#ect
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.ir resistance is a special type o& &rictional &orce that acts upon ob#ects as theytravel through the air
/i2e all &rictional &orces the &orce o& air resistance always opposes the motion o&the ob#ect
%his &orce will &reBuently be ignored due to its negligible magnitude It is mostnoticeable &or ob#ects that travel at high speeds :eg a s2ydiver or a downhills2ier; or &or ob#ects with large sur&ace areas
:$ea li2e a *eep the &unctional eBuivalent o& drive a bric2 with a tent on top downthe highway; :Couldn@t help mysel& I had to add that;
+ensional $orces4
%ension is the &orce that is transmitted through a string rope or wire when it ispulled tight by &orces acting at each end
%he tensional &orce is directed along the wire and pulls eBually on the ob#ects oneither end o& the wire
3.ring $orce
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%he spring &orce is the &orce exerted by a compressed or stretched spring uponany ob#ect that is attached to it
%his &orce acts to restores the ob#ect which compresses or stretches a spring toits rest or eBuilibrium position
-or most springs the magnitude o& the &orce is directly proportional to the amounto& stretch or compression
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