Gradient chart inclines and slopes hill climbing ability


GRADIENT CHART - In this diagram you can see the relationship between a 1:10 slope as being a 10% incline @ roughly 6 degrees, whereas a 30% incline is roughly 17 degrees.


Gradient or steepness of a slope is commonly measured in three ways:

(1) The angle (called the 'slope angle') the line, path, or surface makes with the ground or horizontal (called 'grade line') expressed in degrees. For example, a 6 degree gradient. 

(2) Ratio of the vertical distance to the actual distance along the slope (that is, sine of the slope angle). For example, a gradient of 1 in 4 means a vertical distance of 1 unit for 4 units along the slope, expressed as 1/4 grade or 25% percent grade.

(3) Ratio of the vertical distance (elevation) to the horizontal distance (that is, tangent of the slope angle).


EXAMPLE: If you had a beach that went up by 10 meters over a distance of 100 meters, you would divide the 10 meters by 100 meters to find the slope equals 0.10. Then multiply the 0.10 by 100 to find the gradient to be 10 per cent.




With significant over powering of AmphiMax, the ability to climb a beach is restricted by the traction of the caterpillar tracks on the shingle (soil mechanics), rather than the theoretical gradient climbing lift of the engines. Especially so where a gearbox between the engine and pump allows for even more grunt (if needed) to adapt to a particular beach.


To calculate the power required for a pure vertical lift you need to know that: 0.746 kW (1 horsepower) = 0.305 meters in one second (1ft in 1sec). This is basic information for designing cranes and almost any machine that moves something. It was based on the ability of a real animal to lift or pull a load, long before internal combustion engines were invented. A vertical lift of 0.305m/sec would then require:


2,240 x 100 = 224,000 / 550 = 407hp or 303kW

The "grade" or "incline" of a beach (here assuming a solid medium like a road for rolling resistance purposes) is the rise divided by the distance traveled. You can multiply the incline by the weight of the vehicle to find the force of gravity.


For our 100 ton (total load) amphibian @ 1% gradient that equates to: 2,240 lbs (1,016.4 kg) of gravity force, or 4 horsepower - just to stand still on a 1% slope if you have wheels with good bearings (and no brakes). These are simplistic examples.

On a 2% incline (2/100) we'd need 4,480 lbs (2,032 kg) or 8 horsepower to counteract gravity and on a 20% slopes: 22,400 lbs or 80 horsepower (60kW) to cope with gravity. In practice no beach will be steeper than 30%.


As we may need to be able to deal with up to 30% slopes on a very bad day, we are looking at 120 hp (90kW) as the base motor output + the power to move our load up the beach in a reasonable time and that means speed of travel. In this case 2 - 5mph would be more than adequate, equating to between 300-400kW or (400-535hp). This is for the 100 ton AmphiMax. The smaller AmphiMax would need half that.

Clearly then, the slope of the beach is very important when calculating the power needed to recover SeaVax. Caterpillar tracks are more efficient over shingle. Overly steep shorelines would not provide sufficient traction regardless of any vehicle being tracked because of crumbling, meaning that no amount of power would effect a beaching. Try walking up a steep beach yourself to experience why.


Amphimax beach launching sequence diagram


BEACH LAUNCHING SEQUENCE - Here we see a SeaVax 30 ton filtration boat piggy-backed on an AmphiMax boat launcher as it trundles down a 7 degree beach (10% gradient 1/10) in relation to sea-level, into the sea to begin operations. 


Anything more than a 11 degree beach (20% gradient 1/20) and traction becomes an issue that only caterpillar tracks may tackle. AmphiMax could not climb a 22 degree beach (40% gradient). We doubt if anything could without a lot of difficulty. A 31 degree beach = a 60% slope. See Ice Cold in Alex; a WWII film where they hand crank a truck up a steep sand dune. The steepest roads in the world are Baldwin Street in Dunedin, New Zealand and Canton Avenue in Pittsburgh, Pennsylvania. The Guinness World Record lists Baldwin Street as the steepest street in the world, with a 35% grade (19) overall and disputed 38% grade (21) at its steepest section. The Pittsburgh Department of Engineering and Construction recorded a grade of 37% (20) for Canton Avenue.


The AutoCAD drawings of AmphiMax and SeaVax on this page are Copyright 26 May 2018 Cleaner Ocean Foundation Ltd and Bluebird Marine Systems Ltd. All rights reserved.



The grade (also called slope, incline, gradient, mainfall, pitch or rise) of a physical feature, landform or constructed line refers to the tangent of the angle of that surface to the horizontal. It is a special case of the slope, where zero indicates horizontality. A larger number indicates higher or steeper degree of "tilt". Often slope is calculated as a ratio of "rise" to "run", or as a fraction ("rise over run") in which run is the horizontal distance and rise is the vertical distance.

The grades or slopes of existing physical features such as canyons and hillsides, stream and river banks and beds are often described. Grades are typically specified for new linear constructions (such as roads, landscape grading, roof pitches, railroads, aqueducts, and pedestrian or bicycle circulation routes). The grade may refer to the longitudinal slope or the perpendicular cross slope.

In vehicular engineering, various land-based designs (cars, SUVs, trucks, trains, etc.) are rated for their ability to ascend terrain. Trains typically rate much lower than cars. The highest grade a vehicle can ascend while maintaining a particular speed is sometimes termed that vehicle's "gradeability" (or, less often, "grade ability"). The lateral slopes of a highway geometry are sometimes called fills or cuts where these techniques have been used to create them.

The steepest roads in the world are Baldwin Street in Dunedin, New Zealand and Canton Avenue in Pittsburgh, Pennsylvania. The Guinness World Record lists Baldwin Street as the steepest street in the world, with a 35% grade (19) overall and disputed 38% grade (21) at its steepest section. The Pittsburgh Department of Engineering and Construction recorded a grade of 37% (20) for Canton Avenue.





The AmphiMax is not just a launch and recovery machine, it is an essential development tool for Seavax. We can think of no quicker way to take a boat out of the ocean into a dry dock situation anywhere in the world to allow engineers to fit alternative heads for experimenting full size.


The Amphimax has all the equipment built in to allow a team of engineers to fabricate parts, change machinery and even repair a damaged hull using welding equipment, compressors and generators that are part of the portable dockyard.



Grades and percentages quadrant, angles and degrees ratios


DIAGRAM - This is a useful illustration of grades (percentages), angles in degrees and ratio for easy reference.






540 electric motor and gearbox reduction


540 MOTOR & GEARBOX - The output speed from this motor and gearbox combination is 22 RPM. The 6mm output shaft means a bit more machining at this end, but we feel that it is worth having a reserve of power for our experiments.



Picross precision engineers


PRECISION - Some of the moving parts needed to be engineered beyond the capacity of our workshops. We were very fortunate to have a comprehensively equipped precision engineering company on our doorstep. Picross offer a world class development service from prototype to production. This includes the latest CNC turning and machining centres, precision Tig welding, vacuum leak testing, barcoded bespoke labelling and powder coating, all at competitive prices.


Picross Precision Engineering Co Ltd. 16-18 Lister Road, Eastbourne, BN23 6PU, UK.

Tel: 01323 507322 Email:







 This website is provided on a free basis as a public information service. Copyright Cleaner Oceans Foundation Ltd (COFL) (Company No: 4674774) 2019. Solar Studios, BN271RF, United Kingdom. COFL is a charity without share capital. The names Amphimax, RiverVax and SeaVax are trademarks.