# Fuel consumption formula for license exam **URL:** \ **Category:** Professional Mariner Forum\ **Created:** [February 4, 2020, 6:09pm UTC](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076 "2020-02-04T18:09:21Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Captshane](https://avatars.discourse-cdn.com/v4/letter/c/5f8ce5/32.png) [@Captshane](https://forum.gcaptain.com/u/Captshane)\ **Post date:** [February 4, 2020, 6:09pm UTC](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076/1 "2020-02-04T18:09:21Z")
Can anyone show me how to work this fuel problem, Your vessel consumes 274 bbls of fuel per day at a speed of 17.5 kts. What will be the fuel consumption of your vessel at 13.5 kts. ---
**Author:** ![Kingrobby](https://sea2.discourse-cdn.com/flex016/user_avatar/forum.gcaptain.com/kingrobby/32/68137_2.png) [@Kingrobby](https://forum.gcaptain.com/u/Kingrobby)\ **Post date:** [February 4, 2020, 6:38pm UTC](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076/2 "2020-02-04T18:38:37Z")
I think you’re missing some information to solve this problem accurately. ---
**Author:** ![Kennebec\_Captain](https://sea2.discourse-cdn.com/flex016/user_avatar/forum.gcaptain.com/kennebec_captain/32/13_2.png) [@Kennebec\_Captain](https://forum.gcaptain.com/u/Kennebec_Captain)\ **Post date:** [February 4, 2020, 6:59pm UTC](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076/3 "2020-02-04T18:59:53Z")
cons1/cons2=(v1/v2)^3. cons1 = 274 bbl/day v1 = 17.5 kts v2 = 13.5 kts cons2 = 125.8 bbls /day ---
**Author:** ![Captshane](https://avatars.discourse-cdn.com/v4/letter/c/5f8ce5/32.png) [@Captshane](https://forum.gcaptain.com/u/Captshane)\ **Post date:** [February 4, 2020, 7:24pm UTC](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076/4 "2020-02-04T19:24:14Z")
Thats correct but not understanding how u figuring this problem. How would you do it on a calculator? ---
**Author:** ![Kennebec\_Captain](https://sea2.discourse-cdn.com/flex016/user_avatar/forum.gcaptain.com/kennebec_captain/32/13_2.png) [@Kennebec\_Captain](https://forum.gcaptain.com/u/Kennebec_Captain)\ **Post date:** [February 4, 2020, 7:56pm UTC](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076/5 "2020-02-04T19:56:12Z")
Using algebra. cons1/cons2=(v1/v2)^3. first flip it con2/con1 = (v2/v1)^3 divide v2 by v1 v2/v1 = 13.5/17.5 = 0.7714 get the cube x^3 = x_x_x 0.7714 \* 0.7714 \* 0.7714 = 0.4591 Now you have: con2/con1 = 0.4591 multiply both sides by con1 con2 = (0.4591 \* 274) con2 = 125.8 ---
**Author:** ![Captshane](https://avatars.discourse-cdn.com/v4/letter/c/5f8ce5/32.png) [@Captshane](https://forum.gcaptain.com/u/Captshane)\ **Post date:** [February 4, 2020, 8:06pm UTC](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076/6 "2020-02-04T20:06:16Z")
Thanks so much ---
**Author:** ![Kennebec\_Captain](https://sea2.discourse-cdn.com/flex016/user_avatar/forum.gcaptain.com/kennebec_captain/32/13_2.png) [@Kennebec\_Captain](https://forum.gcaptain.com/u/Kennebec_Captain)\ **Post date:** [February 8, 2020, 11:50am UTC](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076/7 "2020-02-08T11:50:34Z")
Split this topic on February 8, 2020, 11:50am UTC 39 posts were split to a new topic: [Fuel Consumption Not for License Exam](https://forum.gcaptain.com/t/fuel-consumption-not-for-license-exam/54124) ---
**Author:** ![Captshane](https://avatars.discourse-cdn.com/v4/letter/c/5f8ce5/32.png) [@Captshane](https://forum.gcaptain.com/u/Captshane)\ **Post date:** [February 4, 2020, 8:55pm UTC](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076/12 "2020-02-04T20:55:52Z")
Would u use same formula if question asked u if u have enough fuel to travel at 17kts for 775 miles. What speed would u have to go to travel 977 miles. With same amount of fuel. ---
**Author:** ![Captshane](https://avatars.discourse-cdn.com/v4/letter/c/5f8ce5/32.png) [@Captshane](https://forum.gcaptain.com/u/Captshane)\ **Post date:** [February 4, 2020, 9:40pm UTC](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076/15 "2020-02-04T21:40:17Z")
Shipgr Were u answering my question or dutchie? ---
**Author:** ![Kennebec\_Captain](https://sea2.discourse-cdn.com/flex016/user_avatar/forum.gcaptain.com/kennebec_captain/32/13_2.png) [@Kennebec\_Captain](https://forum.gcaptain.com/u/Kennebec_Captain)\ **Post date:** [February 4, 2020, 10:02pm UTC](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076/16 "2020-02-04T22:02:08Z")
No, the formulas are in Merchant Marine Officer’s Handbook, the chapter Engineering for Deck officer. Also maybe in [Richard Plant’s Formula for the Mariner.](https://www.amazon.com/Formulae-Mariner-Richard-Plant/dp/0870333615?tag=gcaptaincom-20) This is the formula you need: Con1/Con2 = (S1^2 \*D1) / (S2^2 \* D2) ---
**Author:** ![Captshane](https://avatars.discourse-cdn.com/v4/letter/c/5f8ce5/32.png) [@Captshane](https://forum.gcaptain.com/u/Captshane)\ **Post date:** [February 4, 2020, 10:21pm UTC](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076/17 "2020-02-04T22:21:06Z")
Thank you sir. Yall been very helpful ---
**Author:** ![shipengr](https://sea2.discourse-cdn.com/flex016/user_avatar/forum.gcaptain.com/shipengr/32/485_2.png) [@shipengr](https://forum.gcaptain.com/u/shipengr)\ **Post date:** [February 4, 2020, 11:54pm UTC](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076/18 "2020-02-04T23:54:05Z")
> [@Captshane](#): > > if u have enough fuel to travel at 17kts for 775 miles. What speed would u have to go to travel 977 miles. With same amount of fuel. > [@Kennebec\_Captain](#): > > This is the formula you need: > > Con1/Con2 = (S1^2 \*D1) / (S2^2 \* D2) Maybe I’m getting myself lost in the numbers, but I don’t see how that formula works for this problem since it doesn’t account for the cube-root curve for the Consumption. The question is asking what speed2 is, and you need speed2 to calculate consumption 2. So you have two missing variables, no? I just used your original con2/con1 = (v2/v1)^3 to solve for consumption@17kt which is 251 bbl/d. At 17kt it would take you 1.89days to go 775nm, multiply by consumption and you’d burn 477bbl. The question then becomes what speed must you go to burn only 477bbl and still make it 977nm. I would plot the consumption for various speeds to interpolate the one that gets you that distance burning less than 477bbl and I get about 15.1 kts. So any speed less than that and you won’t run out of fuel. Did I make that way more difficult than it had to be? ---
**Author:** ![Kennebec\_Captain](https://sea2.discourse-cdn.com/flex016/user_avatar/forum.gcaptain.com/kennebec_captain/32/13_2.png) [@Kennebec\_Captain](https://forum.gcaptain.com/u/Kennebec_Captain)\ **Post date:** [February 5, 2020, 12:10am UTC](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076/19 "2020-02-05T00:10:57Z")
> [@shipengr](#): > > Maybe I’m getting myself lost in the numbers, but I don’t see how that formula works for this problem since it doesn’t account for the cube-root curve for the Consumption The missing “s” (squared accounts for the first two) is hiding in the d because s\*t = d consumption2 is given as the same as con1 so Con1/con2 = 1 ---
**Author:** ![Kennebec\_Captain](https://sea2.discourse-cdn.com/flex016/user_avatar/forum.gcaptain.com/kennebec_captain/32/13_2.png) [@Kennebec\_Captain](https://forum.gcaptain.com/u/Kennebec_Captain)\ **Post date:** [February 5, 2020, 6:56pm UTC](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076/25 "2020-02-05T18:56:42Z")
My copy of the Merchant Maine Officer’s Handbook is a 1980 reprint of the 4th ed, 1965. This is what it says about the formula: page 19-12 _Within 3 knots on either side of the normal speed, in vessels capable of 15 knots, the consumption of fuel varies approximately as the cube of the speed._ ---
**Author:** ![Captshane](https://avatars.discourse-cdn.com/v4/letter/c/5f8ce5/32.png) [@Captshane](https://forum.gcaptain.com/u/Captshane)\ **Post date:** [February 7, 2020, 1:37am UTC](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076/30 "2020-02-07T01:37:54Z")
On the question i have it didnt give any bbls heres the exact question. Your vessel arrives in port with sufficient fuel to steam 775 miles at 17kts. If you are unable to take on bunkers, at what speed must you proceed to reach your next port, 977 miles distant?. The correct answer is 15.1 kts. ---
**Author:** ![Jamesbrown](https://avatars.discourse-cdn.com/v4/letter/j/3d9bf3/32.png) [@Jamesbrown](https://forum.gcaptain.com/u/Jamesbrown)\ **Post date:** [February 7, 2020, 1:50am UTC](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076/31 "2020-02-07T01:50:11Z")
KC’s formula is the one you need and the understanding that con1/con2=1 > [@Kennebec\_Captain](#): > > This is the formula you need: > > Con1/Con2 = (S1^2 \*D1) / (S2^2 \* D2) So 1 = (S1^2 \*D1) / (S2^2 \* D2) (Multiply denominator on both sides of equation) (S2^2 \* D2)= (S1^2 \*D1) divide both sides by D2 and take square root S2 =Sqrt [(S1^2 \*D1)/D2] ---
**Author:** ![Captshane](https://avatars.discourse-cdn.com/v4/letter/c/5f8ce5/32.png) [@Captshane](https://forum.gcaptain.com/u/Captshane)\ **Post date:** [February 7, 2020, 2:00am UTC](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076/32 "2020-02-07T02:00:15Z")
Dont follow how u have a second speed, when thats what im looking for, but please correct me if im wrong. Problem only has 17kts to work with. ---
**Author:** ![Jamesbrown](https://avatars.discourse-cdn.com/v4/letter/j/3d9bf3/32.png) [@Jamesbrown](https://forum.gcaptain.com/u/Jamesbrown)\ **Post date:** [February 7, 2020, 2:13am UTC](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076/33 "2020-02-07T02:13:23Z")
S1=17 knots, you have D1, you have D2 and want to find S2 which you say is 15.1 knots. To solve for a quantity in algebra, you rearrange the formulas to isolate the unknown on one side of the equation and solve using the knowns. ---
**Author:** ![Kennebec\_Captain](https://sea2.discourse-cdn.com/flex016/user_avatar/forum.gcaptain.com/kennebec_captain/32/13_2.png) [@Kennebec\_Captain](https://forum.gcaptain.com/u/Kennebec_Captain)\ **Post date:** [February 7, 2020, 11:15am UTC](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076/34 "2020-02-07T11:15:04Z")
This is simpler if it can be seen that Con1/Con1 = 1 but if not then a little longer way round: there are two unknowns and two equations. 1. This is from the book: Con1/Con2 = (S1^2 \*D1) / (S2^2 \* D2) 2. This is given: Con1 = Con2 Given Con1 = Con2 then #2 equation can substitute: Con1/Con1 = (S1^2 \*D1) / (S2^2 \* D2) For Con1 ≠ 0 :then Con1/Con1 = 1 1 = (S1^2 \*D1) / (S2^2 \* D2) Then rearrange to solve for S2 which has already been shown. D1 = 775 miles D2 = 977 miles S1 = 17 kts ---
**Author:** ![portofdc](https://avatars.discourse-cdn.com/v4/letter/p/8797f3/32.png) [@portofdc](https://forum.gcaptain.com/u/portofdc)\ **Post date:** [February 7, 2020, 11:21am UTC](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076/35 "2020-02-07T11:21:32Z")
I posted this site once before, but the address has changed. Go to [https://curiousbensite.wordpress.com/](https://curiousbensite.wordpress.com/) This guy did a great explanation of fuel conservation problems including a video. There are also some additional tips for the exam. [Next page](https://forum.gcaptain.com/t/fuel-consumption-formula-for-license-exam/54076.md?page=2)