Drill collar provides weight to the bit for drilling and keep the drill string from buckling. Additionally, drill pipe should not run in compression because it can get seriously damaged therefore we need to know weight of drill collar that is enough to provide weight to the bit.
Drill pipe buckle due to insufficient of drill collar
Drill pipe straight because of sufficient drill collar weight
Drill collar weight in a vertical well
The following formula is used to determine required drill collar weight to obtain a desired weight on bit for a vertical well.
WDC = (WOB x SF) ÷ BF
Where
WDC is drill collar weight in air, lb.
WOB is a required weight on bit, lb.
SF is a safety factor.
BF is mud buoyancy factor.
Drill collar weight in a deviated well
In a deviated well, the drill collar weight will not directly transfer to the bit because of well inclination which has direct affect on weight on bit.
The following formula is used to determine required drill collar weight to obtain a desired weight on bit for a deviated well.
WDC = (WOB x SF) ÷ (BF x COS (θ))
Where
WDC is drill collar weight in air, lb.
WOB is a required weight on bit, lb.
SF is a safety factor.
BF is mud buoyancy factor.
θ is inclination of the well.
Example: The deviated well has inclination of 30 degree in tangent section and planned mud weight is 12.0 ppg. Safety factor for this case is 25%.
What is the drill collar weight to obtain the desired WOB of 50 Klb?
Buoyancy Factor = (65.5 – 12.0) ÷ 65.5 = 0.817
SF @ 25 % = 1.25
WDC = (50,000 x 1.25) ÷ (0.817 x COS (30))
WDC = 88,333 Klb
In this case, drill collar weight in the air should be 88.3 Klb. In reality, the BHA does not only have the drill collar so you need to adapt this figure. For instant, the BHA consists of mud motor, stabilizer, LWD and HWDP which have a total weight of 30 Klb. Therefore, the actual drill collar weight is just only 58.3 Klb (88.3 – 30).
Ref Book: 
Formulas and Calculations for Drilling, Production and Workover, Second Edition